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Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO. (English) Zbl 1346.90677
Summary: This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

MSC:
90C26 Nonconvex programming, global optimization
90C11 Mixed integer programming
90C56 Derivative-free methods and methods using generalized derivatives
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
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References:
[1] Abramson, M. A., Pattern search algorithms for mixed variable general constrained optimization problems, (2002), Ecole Polytechnique de Montreal, Ph.D. thesis
[2] Abramson, M. A.; Asaki, T. J.; Dennis, J. E.; O’Reilly, K. R.; Pingel, R. L., Quantitative object reconstruction using Abel transform X-ray tomography and mixed variable optimization, The SIAM Journal on Imaging Sciences, 1, 3, 322-342, (2008) · Zbl 1177.65200
[3] Abramson, M. A.; Asaki, T. J.; Jr., J. E.D.; Jr., R. M.; Sottile, M. J., An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions, Structural and Multidisciplinary Optimization, 45, 1, 53-64, (2012) · Zbl 1274.74006
[4] Abramson, M. A.; Audet, C., Convergence of mesh adaptive direct search to second-order stationary points, The SIAM Journal on Optimization, 17, 2, 606-619, (2006) · Zbl 1174.90877
[5] Abramson, M. A.; Audet, C.; Chrissis, J. W.; Walston, J. G., Mesh adaptive direct search algorithms for mixed variable optimization, Optimization Letters, 3, 1, 35-47, (2009) · Zbl 1154.90551
[6] Abramson, M. A., Audet, C., Couture, G., Dennis, J. E., Le Digabel, S. Tribes, C.(2009b). The NOMAD project. Available at: http://www.gerad.ca/nomad.
[7] Abramson, M. A.; Audet, C.; Dennis, J. E., Filter pattern search algorithms for mixed variable constrained optimization problems, The SIAM Journal on Optimization, 11, 3, 573-594, (2001)
[8] Abramson, M. A.; Audet, C.; Dennis, J. E.; Le Digabel, S., Orthomads: A deterministic MADS instance with orthogonal directions, The SIAM Journal on Optimization, 20, 2, 948-966, (2009) · Zbl 1189.90202
[9] Achterberg, T., SCIP: solving constraint integer programs, Mathematical Programming Computation, 1, 1, 1-41, (2009) · Zbl 1171.90476
[10] Achterberg, T.; Berthold, T.; Koch, T.; Wolter, K., Constraint integer programming: a new approach to integrate CP and MIP, Integration of AI and or techniques in constraint programming for combinatorial optimization problems, (2008) · Zbl 1142.68504
[11] Achterberg, T.; Koch, T.; Martin, A., Branching rules revisited, Operations Research Letters, 33, 1, 42-54, (2005) · Zbl 1076.90037
[12] Adjengue, L.; Audet, C.; Yahia, I. B., A variance-based method to rank input variables of the mesh adaptive direct search algorithm, Optimization Letters, 8, 5, 1599-1610, (2013) · Zbl 1303.90125
[13] Adjiman, C. S.; Androulakis, I. P.; Floudas, C. A., A global optimization method, αBB, for general twice differentiable NLPs-II. implementation and computional results, Computers & Chemical Engineering, 22, 1159-1179, (1998)
[14] Adjiman, C. S.; Androulakis, I. P.; Floudas, C. A., Global optimization of mixed-integer nonlinear problems, AIChE Journal, 46, 9, 1769-1797, (2000)
[15] Adjiman, C. S.; Dallwig, S.; Floudas, C. A.; Neumaier, A., A global optimization method, αBB, for general twice differentiable NLPs-I. theoretical advances, Computers & Chemical Engineering, 22, 1137-1158, (1998)
[16] Agarwal, A.; Biegler, L. T., A trust-region framework for constrained optimization using reduced order modeling, Optimization and Engineering, 14, 1, 3-35, (2013) · Zbl 1293.76109
[17] Aggarwal, A.; Floudas, C. A., Synthesis of general distillation sequences - nonsharp separations, Computers & Chemical Engineering, 14, 6, 631-653, (1990)
[18] Ahmetović, E. Grossmann, I. E. (2010). Integrated process water networks design problem. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=101.
[19] Ahmetović, E.; Grossmann, I. E., Global superstructure optimization for the design of integrated process water networks, AIChE Journal, 57, 2, 434-457, (2011)
[20] Akrotirianakis, I. G.; Floudas, C. A., Computational experience with a new class of convex underestimators: box-constrained NLP problems, Journal of Global Optimization, 29, 3, 249-264, (2004) · Zbl 1133.90420
[21] Akrotirianakis, I. G.; Floudas, C. A., A new class of improved convex underestimators for twice continuously differentiable constrained nlps, Journal of Global Optimization, 30, 4, 367-390, (2004) · Zbl 1082.90090
[22] Akrotirianakis, I. G.; Meyer, C. A.; Floudas, C. A., The role of the off-diagonal elements of the Hessian matrix in the construction of tight convex underestimators for nonconvex functions, Discovery through product and process design, 501-504, (2004), Foundations of Computer-Aided Process Design
[23] Al-Khayyal, F. A.; Falk, J. E., Jointly constrained biconvex programming, Mathematics of Operations Research, 8, 2, 273-286, (1983) · Zbl 0521.90087
[24] Alfaki, M.; Haugland, D., A multi-commodity flow formulation for the generalized pooling problem, Journal of Global Optimization, 56, 3, 917-937, (2013) · Zbl 1272.90103
[25] Amaral, P.; Bomze, I. M.; Júdice, J., Copositivity and constrained fractional quadratic problems, Mathematical Programming, 146, 1-2, 325-350, (2014) · Zbl 1312.90049
[26] Androulakis, I. P.; Maranas, C. D.; Floudas, C. A., αBB: A global optimization method for general constrained nonconvex problems, Journal of Global Optimization, 7, 337-363, (1995) · Zbl 0846.90087
[27] Anjos, M. F.; Liers, F., Global approaches for facility layout and VLSI floorplanning, (Anjos, M. F.; Lasserre, J. B., Handbook on semidefinite, conic and polynomial optimization, International Series in Operations Research & Management Science, 166, (2012), Springer US), 849-877 · Zbl 1334.90096
[28] Anstreicher, K. M., Recent advances in the solution of quadratic assignment problems, Mathematical Programming, 97, 1-2, 27-42, (2003) · Zbl 1035.90067
[29] Anstreicher, K. M., Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming, Journal of Global Optimization, 43, 2-3, 471-484, (2009) · Zbl 1169.90425
[30] Anstreicher, K. M.; Burer, S., Computable representations for convex hulls of low-dimensional quadratic forms, Mathematical Programming, 124, 1-2, 33-43, (2010) · Zbl 1198.90311
[31] Arouxét, M. B.; Echebest, N. E.; Pilotta, E. A., Inexact restoration method for nonlinear optimization without derivatives, Journal of Computational and Applied Mathematics, 290, 26-43, (2015) · Zbl 1321.65093
[32] Audet, C.; Béchard, V.; Chaouki, J., Spent potliner treatment process optimization using a MADS algorithm, Optimization and Engineering, 9, 2, 143-160, (2008) · Zbl 1167.92039
[33] Audet, C.; Béchard, V.; Le Digabel, S., Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search, Journal of Global Optimization, 41, 2, 299-318, (2008) · Zbl 1157.90535
[34] Audet, C.; Brimberg, J.; Hansen, P.; Le Digabel, S.; Mladenovic, N., Pooling problem: alternate formulations and solution methods, Management Science, 50, 6, 761-776, (2004) · Zbl 1232.90349
[35] Audet, C.; Dennis, J. E., Pattern search algorithms for mixed variable programming, The SIAM Journal on Optimization, 11, 3, 573-594, (2001) · Zbl 1035.90048
[36] Audet, C.; Dennis, J. E., Analysis of generalized pattern searches, The SIAM Journal on Optimization, 13, 3, 889-903, (2002) · Zbl 1053.90118
[37] Audet, C.; Dennis, J. E., A pattern search filter method for nonlinear programming without derivatives, The SIAM Journal on Optimization, 14, 4, 980-1010, (2004) · Zbl 1073.90066
[38] Audet, C.; Dennis, J. E., Mesh adaptive direct search algorithms for constrained optimization, The SIAM Journal on Optimization, 17, 1, 188-217, (2006) · Zbl 1112.90078
[39] Audet, C.; Dennis, J. E., A progressive barrier for derivative-free nonlinear programming, The SIAM Journal on Optimization, 20, 1, 445-472, (2009) · Zbl 1187.90266
[40] Audet, C.; Dennis, J. E.; Le Digabel, S., Parallel space decomposition of the mesh adaptive direct search algorithm, The SIAM Journal on Optimization, 19, 3, 1150-1170, (2008) · Zbl 1180.90363
[41] Audet, C.; Dennis, J. E.; Le Digabel, S., Globalization strategies for mesh adaptive direct search, Computational Optimization and Applications, 46, 2, 193-215, (2010) · Zbl 1190.90204
[42] Audet, C.; Guillou, A.; Hansen, P.; Messine, F.; Perron, S., The small hexagon and heptagon with maximum sum of distances between vertices, Journal of Global Optimization, 49, 3, 467-480, (2011) · Zbl 1211.90258
[43] Audet, C.; Hansen, P.; Jaumard, B.; Savard, G., A branch and cut algorithm for nonconvex quadratically constrained quadratic programming, Mathematical Programming, 87, 1, 131-152, (2000) · Zbl 0966.90057
[44] Audet, C.; Hansen, P.; Messine, F., The small octagon with longest perimeter, Journal of Combinatorial Theory, Series A, 114, 1, 135-150, (2007) · Zbl 1259.90096
[45] Audet, C.; Hansen, P.; Messine, F., Simple polygons of maximum perimeter contained in a unit disk, Discrete & Computational Geometry, 41, 2, 208-215, (2009) · Zbl 1166.52003
[46] Audet, C.; Hansen, P.; Messine, F.; Xiong, J., The largest small octagon, Journal of Combinatorial Theory, Series A, 98, 1, 46-59, (2002) · Zbl 1022.90013
[47] Audet, C.; Ianni, I.; Le Dibagel, S.; Tribes, C., Reducing the number of function evaluations in mesh adaptive direct search algorithms, The SIAM Journal on Optimization, 24, 2, 621-642, (2014) · Zbl 1297.90149
[48] Audet, C.; Ninin, J., Maximal perimeter, diameter and area of equilateral unit-width convex polygons, Journal of Global Optimization, 56, 3, 1007-1016, (2013) · Zbl 1272.90055
[49] Bagajewicz, M., A review of recent design procedures for water networks in refineries and process plants, Computers & Chemical Engineering, 24, 2093-2113, (2000)
[50] Baliban, R. C.; Elia, J. A.; Floudas, C. A., Biomass to liquid transportation fuels (BTL) systems: process synthesis and global optimization framework, Energy & Environmental Science, 6, 1, 267-287, (2013)
[51] Baliban, R. C.; Elia, J. A.; Floudas, C. A., Novel natural gas to liquids processes: process synthesis and global optimization strategies, AIChE Journal, 59, 2, 505-531, (2013)
[52] Baliban, R. C.; Elia, J. A.; Misener, R.; Floudas, C. A., Global optimization of a MINLP process synthesis model for thermochemical based conversion of hybrid coal, biomass, and natural gas to liquid fuels, Computers & Chemical Engineering, 42, 64-86, (2012)
[53] Baliban, R. C.; Elia, J. A.; Weekman, V.; Floudas, C. A., Process synthesis of hybrid coal, biomass, and natural gas to liquids via fischer-tropsch synthesis, ZSM-5 catalytic conversion, methanol synthesis, methanol-to-gasoline, and methanol-to-olefins/distillate technologies, Computers & Chemical Engineering, 47, 29-56, (2012)
[54] Ballerstein, M.; Michaels, D., Extended formulations for convex envelopes, Journal of Global Optimization, 60, 2, 217-238, (2014) · Zbl 1335.90070
[55] Banga, J. R.; Balsa-Canto, E.; Moles, C. G.; Alonso, A. A., Dynamic optimization of bioprocesses: efficient and robust numerical strategies, Journal of Biotechnology, 117, 4, 407-419, (2005)
[56] Banga, J. R.; Irizarry-Rivera, R.; Seider, W. D., Stochastic optimization for optimal and model-predictive control, Computers & Chemical Engineering, 22, 4-5, 603-612, (1998)
[57] Bao, X.; Sahinidis, N. V.; Tawarmalani, M., Multiterm polyhedral relaxations for nonconvex, quadratically-constrained quadratic programs, Optimization Methods and Software, 24, 4-5, 485-504, (2009) · Zbl 1179.90252
[58] Bao, X.; Sahinidis, N. V.; Tawarmalani, M., Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons, Mathematical Programming, 129, 1, 129-157, (2011) · Zbl 1232.49035
[59] Bartholomew-Biggs, M. C.; Parkhurst, S. C.; Wilson, S. P., Using DIRECT to solve an aircraft routing problem, Computational Optimization and Applications, 21, 3, 311-323, (2002) · Zbl 1017.90133
[60] Bartholomew-Biggs, M. C.; Parkhurst, S. C.; Wilson, S. P., Global optimization approaches to an aircraft routing problem, European Journal of Operational Research, 146, 2, 417-431, (2003) · Zbl 1012.90037
[61] Belotti, P., Bound reduction using pairs of linear inequalities, Journal of Global Optimization, 56, 3, SI, 787-819, (2013) · Zbl 1272.90033
[62] Belotti, P.; Cafieri, S.; Lee, J.; Liberti, L., Feasibility-based bounds tightening via fixed points, (Wu, W.; Daescu, O., Combinatorial optimization and applications, Lecture Notes in Computer Science, 6508, (2010), Springer Berlin Heidelberg), 65-76 · Zbl 1311.90189
[63] Belotti, P., Cafieri, S., Lee, J. Liberti, L. (2012). On feasibility based bounds tightening. http://www.optimization-online.org/DB_HTML/2012/01/3325.html. · Zbl 1311.90189
[64] Belotti, P.; Cafieri, S.; Lee, J.; Liberti, L.; Miller, A., On the composition of convex envelopes for quadrilinear terms, (Chinchuluun, A.; Pardalos, P. M.; Enkhbat, R.; Pistikopoulos, E. N., Optimization, simulation, and control, Springer Optimization and Its Applications, 76, (2013), Springer New York), 1-16 · Zbl 1309.90062
[65] Belotti, P.; Kirches, C.; Leyffer, S.; Linderoth, J.; Luedtke, J.; Mahajan, A., Mixed-integer nonlinear optimization, Acta Numerica, 22, 1-131, (2013) · Zbl 1291.65172
[66] Belotti, P.; Lee, J.; Liberti, L.; Margot, F.; Wächter, A., Branching and bounds tightening techniques for non-convex MINLP, Optimization Methods and Software, 24, 4-5, 597-634, (2009) · Zbl 1179.90237
[67] Belotti, P.; Miller, A. J.; Namazifar, M., Valid inequalities and convex hulls for multilinear functions. electronic notes in discrete mathematics, Proceedings of the international symposium on combinatorial optimization ISCO, 2010, 36, 805-812, (2010) · Zbl 1274.90499
[68] Ben-Tal, A.; Eiger, G.; Gershovitz, V., Global minimization by reducing the duality gap, Mathematical Programming, 63, 193-212, (1994) · Zbl 0807.90101
[69] Benson, H. P., On the construction of convex and concave envelope formulas for bilinear and fractional functions on quadrilaterals, Computational Optimization and Applications, 27, 1, 5-22, (2004) · Zbl 1045.90068
[70] Bergamini, M. L.; Grossmann, I.; Scenna, N.; Aguirre, P., An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms, Computers & Chemical Engineering, 32, 3, 477-493, (2008)
[71] Berthold, T., RENS - the optimal rounding, Mathematical Programming Computation, 6, 33-54, (2013) · Zbl 1304.90147
[72] Berthold, T., Heuristic algorithms in global MINLP solvers, (2014), (Ph.D. in Mathematics). Technischen Universität Berlin
[73] Berthold, T.; Gleixner, A. M., Undercover: a primal MINLP heuristic exploring a largest sub-MIP, Mathematical Programming, 144, 315-346, (2013) · Zbl 1291.90144
[74] Berthold, T.; Gleixner, A. M., Undercover branching, (Bonifaci, V.; Demetrescu, C.; Marchetti-Spaccamela, A., Experimental algorithms, Lecture Notes in Computer Science, 7933, (2013), Springer Berlin Heidelberg), 212-223
[75] Berthold, T.; Gleixner, A. M.; Heinz, S.; Vigerske, S., Analyzing the computational impact of MIQCP solver components, Numerical Algebra, Control and Optimization, 2, 4, 739-748, (2012) · Zbl 1269.90066
[76] Berthold, T.; Heinz, S.; Vigerske, S., Extending a CIP framework to solve miqcps, (Lee, J.; Leyffer, S., Mixed integer nonlinear programming, The IMA Volumes in Mathematics and its Applications, 154, (2012), Springer New York), 427-444 · Zbl 1242.90120
[77] Biegler, L. T.; Grossmann, I. E., Retrospective on optimization, Computers & Chemical Engineering, 28, 8, 1169-1192, (2004)
[78] Bienstock, D.; Michalka, A., Cutting-planes for optimization of convex functions over nonconvex sets, The SIAM Journal on Optimization, 24, 2, 643-677, (2014) · Zbl 1334.90130
[79] Björkman, M.; Holmström, K., Global optimization of costly nonconvex functions using radial basis functions, Optimization and Engineering, 1, 4, 373-397, (2000) · Zbl 1035.90061
[80] Bley, A.; Gleixner, A. M.; Koch, T.; Vigerske, S., Comparing MIQCP solvers to a specialised algorithm for mine production scheduling, (Bock, H. G.; Hoang, X. P.; Rannacher, R.; Schlöder, J. P., Modeling, simulation and optimization of complex processes, (2012), Springer Berlin Heidelberg), 25-39
[81] Boland, N.; Eberhard, A.; Engineer, F.; Tsoukalas, A., A new approach to the feasibility pump in mixed integer programming, The SIAM Journal on Optimization, 22, 3, 831-861, (2012) · Zbl 1277.90077
[82] Bompadre, A.; Mitsos, A., Convergence rate of mccormick relaxations, Journal of Global Optimization, 52, 1, 1-28, (2011) · Zbl 1257.90077
[83] Bomze, I. M., Copositive optimization: recent developments and applications, European Journal of Operational Research, 216, 3, 509-520, (2012) · Zbl 1262.90129
[84] Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M., The maximum clique problem, (Du, D.-Z.; Pardalos, P. M., Handbook of combinatorial optimization, (1999), Springer US), 1-74 · Zbl 1253.90188
[85] Bonami, P.; Biegler, L. T.; Conn, A. R.; Cornuéjols, G.; Grossmann, I. E.; Laird, C. D.; Wächter, A., An algorithmic framework for convex mixed integer nonlinear programs, Discrete Optimization, 5, 2, 186-204, (2008) · Zbl 1151.90028
[86] Bonami, P.; Olivares, A.; Soler, M.; Staffetti, E., Multiphase mixed-integer optimal control approach to aircraft trajectory optimization, Journal of Guidance, Control, and Dynamics, 36, 5, 1267-1277, (2013)
[87] Bonilla-Petriciolet, A.; Iglesias-Silva, G. A.; Hall, K. R., Calculation of homogeneous azeotropes in reactive and non-reactive mixtures using a stochastic optimization approach, Fluid Phase Equilibria, 281, 1, 22-31, (2009)
[88] Bonilla-Petriciolet, A.; Rangaiah, G. P.; Segovia-Hernandez, J. G., Evaluation of stochastic global optimization methods for modeling vapor-liquid equilibrium data, Fluid Phase Equilibria, 287, 2, 111-125, (2010)
[89] Booker, A. J.; Dennis, J. E.; Frank, P. D.; Serafini, D. B.; Torczon, V.; Trosset, M. W., A rigorous framework for optimization of expensive functions by surrogates, Structural and Multidisciplinary Optimization, 17, 1, 1-13, (1999)
[90] Boukouvala, F.; Hasan, M. M.F.; Floudas, C. A., Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption, Journlal of Global Optimization, 1-40, (2015)
[91] Boukouvala, F.; Ierapetritou, M. G., Surrogate-based optimization of expensive flowsheet modeling for continuous pharmaceutical manufacturing, Journal of Pharmaceutical Innovation, 8, 2, 131-145, (2013)
[92] Boukouvala, F.; Ierapetritou, M. G., Derivative-free optimization for expensive constrained problems using a novel expected improvement objective function, AIChE Journal, 60, 7, 2462-2474, (2014)
[93] Box, M. J., A new method of constrained optimization and a comparison with other methods, Computer Journal, 8, 1, 42-52, (1965) · Zbl 0142.11305
[94] Bragalli, C.; D’Ambrosio, C.; Lee, J.; Lodi, A.; Toth, P., On the optimal design of water distribution networks: A practical MINLP approach, Optimization and Engineering, 13, 219-246, (2012) · Zbl 1293.76045
[95] Brekelmans, R.; Driessen, L.; Hamers, H.; den Hertog, D., Constrained optimization involving expensive function evaluations: A sequential approach, European Journal of Operational Research, 160, 1, 121-138, (2005) · Zbl 1067.90151
[96] Brönnimann, H.; Melquiond, G.; Pion, S., The boost interval arithmetic library, Proceedings of the 5th conference on real numbers and computers, Lyon, France, 65-80, (2003)
[97] Brönnimann, H.; Melquiond, G.; Pion, S., The design of the boost interval arithmetic library, Theoretical Computer Science, 351, 111-118, (2006) · Zbl 1086.65046
[98] Bruno, J. C.; Fernandez, F.; Castells, F.; Grossmann, I. E., A rigorous MINLP model for the optimal synthesis and operation of utility plants, Chemical Engineering Research and Design, 76, 3, 246-258, (1998)
[99] Burer, S.; Letchford, A. N., Non-convex mixed-integer nonlinear programming: A survey, Surveys in Operations Research and Management Science, 17, 2, 97-106, (2012)
[100] Burer, S.; Saxena, A., The MILP road to MIQCP, (Lee, J.; Leyffer, S., Mixed integer nonlinear programming, The IMA Volumes in Mathematics and its Applications, 154, (2012), Springer New York), 373-405 · Zbl 1242.90122
[101] Burer, S.; Vandenbussche, D., A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations, Mathematical Programming, 113, 2, 259-282, (2008) · Zbl 1135.90034
[102] Bussieck, M. R.; Drud, A. S.; Meeraus, A., Minlplib - a collection of test models for mixed-integer nonlinear programming, INFORMS Journal on Computing, 15, 1, 114-119, (2003) · Zbl 1238.90104
[103] Bussieck, M. R.; Vigerske, S., MINLP solver software, (Cochran, J. J.; Cox, L. A.; Keskinocak, P.; Kharoufeh, J. P.; Smith, J. C., Wiley encyclopedia of operations research and management science, (2010), John Wiley & Sons, Inc.)
[104] Caballero, J. A.; Grossmann, I. E., Generalized disjunctive programming model for the optimal synthesis of thermally linked distillation columns, Industrial & Engineering Chemistry Research, 40, 10, 2260-2274, (2001)
[105] Caballero, J. A.; Grossmann, I. E., Design of distillation sequences: from conventional to fully thermally coupled distillation systems, Computers & Chemical Engineering, 28, 11, 2307-2329, (2004)
[106] Caballero, J. A.; Grossmann, I. E., Structural considerations and modeling in the synthesis of heat integrated thermally coupled distillation sequences, Industrial & Engineering Chemistry Research, 45, 25, 8454-8474, (2006)
[107] Caballero, J. A.; Grossmann, I. E., An algorithm for the use of surrogate models in modular flowsheet optimization, AIChE Journal, 54, 10, 2633-2650, (2008)
[108] Caballero, J. A. Grossmann, I. E. (2009). Optimal separation sequences based on distillation: From conventional to fully thermally coupled systems. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=69.
[109] Cafieri, S.; Durand, N., Aircraft deconfliction with speed regulation: new models from mixed-integer optimization, Journal of Global Optimization, 58, 4, 613-629, (2014) · Zbl 1301.90062
[110] Cafieri, S.; Hansen, P.; Létocart, L.; Liberti, L.; Messine, F., Compact relaxations for polynomial programming problems, (Klasing, R., Experimental algorithms, Lecture Notes in Computer Science, 7276, (2012), Springer, Berlin), 75-86
[111] Cafieri, S.; Lee, J.; Liberti, L., On convex relaxations of quadrilinear terms, Journal of Global Optimization, 47, 661-685, (2010) · Zbl 1202.90236
[112] Cambini, R.; Sodini, C., Decomposition methods for solving nonconvex quadratic programs via branch and bound, Journal of Global Optimization, 33, 313-336, (2005) · Zbl 1093.90034
[113] Caprara, A.; Locatelli, M., Global optimization problems and domain reduction strategies, Mathematical Programming, 125, 1, 123-137, (2010) · Zbl 1198.90325
[114] Castillo, I.; Westerlund, J.; Emet, S.; Westerlund, T., Optimization of block layout design problems with unequal areas: A comparison of MILP and MINLP optimization methods, Computers & Chemical Engineering, 30, 1, 54-69, (2005)
[115] Castillo, P. A.C.; Mahalec, V.; Kelly, J. D., Inventory pinch algorithm for gasoline blend planning, AIChE Journal, 59, 10, 3748-3766, (2013)
[116] Castro, P.; Novais, A., Optimal periodic scheduling of multistage continuous plants with single and multiple time grid formulations, Industrial & Engineering Chemistry Research, 46, 11, 3669-3683, (2007)
[117] Castro, P. Novais, A. (2009). Periodic scheduling of continuous multiproduct plants. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=34.
[118] Castro, P. M.; Matos, H. A.; Novais, A. Q., An efficient heuristic procedure for the optimal design of wastewater treatment systems, Resources, Conservation and Recycling, 50, 2, 158-185, (2007)
[119] Castro, P. M.; Teles, J. P., Comparison of global optimization algorithms for the design of water-using networks, Computers & Chemical Engineering, 52, 249-261, (2013)
[120] Castro, P. M.; Teles, J. P.; Novais, A. Q., Linear program-based algorithm for the optimal design of wastewater treatment systems, Clean Technologies and Environmental Policy, 11, 1, 83-93, (2009)
[121] Chang, Y. J.; Sahinidis, N. V., Optimization of metabolic pathways under stability considerations, Computers & Chemical Engineering, 29, 3, 467-479, (2005)
[122] Chang, Y. J.; Sahinidis, N. V., Global optimization in stabilizing controller design, Journal of Global Optimization, 38, 509-526, (2007) · Zbl 1125.93461
[123] Chang, Y. J. Sahinidis, N. V. (2009). Stabilizing controller design and the Belgian chocolate problem. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=57.
[124] Ciric, A. R.; Floudas, C. A., A retrofit approach for heat exchanger networks, Computers & Chemical Engineering, 13, 6, 703-715, (1989)
[125] Colmenares, T. R.; Seider, W. D., Synthesis of utility systems integrated with chemical processes, Industrial & Engineering Chemistry Research, 28, 1, 84-93, (1989)
[126] Conejo, P. D.; Karas, E. W.; Pedroso, L. G.; Ribeiro, A. A.; Sachine, M., Global convergence of trust-region algorithms for convex constrained minimization without derivatives, Applied Mathematics and Computation, 220, 324-330, (2013) · Zbl 1329.90170
[127] Conn, A. R.; Le Digabel, S., Use of quadratic models with mesh-adaptive direct search for constrained black box optimization, Optimization Methods and Software, 28, 1, 139-158, (2013) · Zbl 1270.90073
[128] Conn, A. R.; Scheinberg, K.; Vicente, L. N., Global convergence of general derivative-free trust-region algorithms to first and second order critical points, The SIAM Journal on Optimization, 20, 387-415, (2009) · Zbl 1187.65062
[129] Conn, A. R.; Scheinberg, K.; Vicente, L. N., Introduction to derivative-free optimization, MPS-SIAM Series on Optimization, (2009), SIAM Philadelphia · Zbl 1163.49001
[130] Csendes, T.; Pal, L.; Sendin, J. O.H.; Banga, J. R., The GLOBAL optimization method revisited, Optimization Letters, 2, 4, 445-454, (2008) · Zbl 1160.90660
[131] Custódio, A.; Madeira, J., Glods: global and local optimization using direct search, Journal of Global Optimization, 62, 1, 1-28, (2015) · Zbl 1328.90161
[132] Custódio, A. L.; Dennis, J. E.; Vicente, L. N., Using simplex gradients of nonsmooth functions in direct search methods, IMA Journal of Numerical Analysis, 28, 4, 770-784, (2008) · Zbl 1156.65059
[133] Dahdah, T. H.; Mitsos, A., Structural optimization of seawater desalination: I. a flexible superstructure and novel MED-MSF configurations, Desalination, 344, 252-265, (2014)
[134] Dahdah, T. H.; Mitsos, A., Structural optimization of seawater desalination: II novel MED MSF TVC configurations, Desalination, 344, 219-227, (2014)
[135] Dalkiran, E.; Sherali, H. D., Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality, Journal of Global Optimization, 57, 4, 1147-1172, (2013) · Zbl 1282.90134
[136] D’Ambrosio, C., Bragalli, C., Lee, J., Lodi, A. Toth, P.(2011a). Optimal design of water distribution networks. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=134.
[137] D’Ambrosio, C.; Frangioni, A.; Liberti, L.; Lodi, A., On interval-subgradient and no-good cuts, Operations Research Letters, 38, 5, 341-345, (2010) · Zbl 1202.90238
[138] D’Ambrosio, C.; Frangioni, A.; Liberti, L.; Lodi, A., A storm of feasibility pumps for nonconvex MINLP, Mathematical Programming, 136, 375-402, (2012) · Zbl 1257.90056
[139] D’Ambrosio, C.; Linderoth, J.; Luedtke, J., Valid inequalities for the pooling problem with binary variables, (Günlük, O.; Woeginger, G. J., Integer programming and combinatoral optimization, Lecture Notes in Computer Science, 6655, (2011), Springer Berlin Heidelberg), 117-129 · Zbl 1339.90238
[140] D’Ambrosio, C.; Lodi, A., Mixed integer nonlinear programming tools: an updated practical overview, Annals of Operations Research, 204, 301-320, (2013) · Zbl 1269.90067
[141] Das, S.; Suganthan, P. N., Differential evolution: A survey of the state-of-the-art, IEEE Transactions on Evolutionary Computation, 15, 1, 4-31, (2011)
[142] Davis, E.; Ierapetritou, M. G., A Kriging method for the solution of nonlinear programs with black-box functions, AIChE Journal, 53, 8, 2001-2012, (2007)
[143] Davis, E.; Ierapetritou, M. G., A Kriging-based approach to MINLP containing black-box models and noise, Industrial & Engineering Chemistry Research, 47, 16, 6101-6125, (2008)
[144] Davis, E.; Ierapetritou, M. G., A Kriging based method for the solution of mixed-integer nonlinear programs containing black-box functions, Journal of Global Optimization, 43, 2-3, 191-205, (2009) · Zbl 1179.90238
[145] de Moura, L.; Passmore, G. O., Computation in real closed infinitesimal and transcendental extensions of the rationals, (Bonacina, M. P., Automated deduction CADE-24, Lecture Notes in Computer Science, Vol. 7898, (2013), Springer Berlin Heidelberg), 178-192 · Zbl 1381.68278
[146] De Servi, C.; Campanari, S.; Tizzanini, A.; Pietra, C., Enhancement of the electrical efficiency of commercial fuel cell units by means of an organic rankine cycle: a case study, Journal of Engineering for Gas Turbines and Power, 135, 4, 042309, (2013)
[147] Deng, Z.; Bai, Y.; Fang, S.-C.; Tian, Y.; Xing, W., A branch-and-cut approach to portfolio selection with marginal risk control in a linear conic programming framework, Journal of Systems Science and Systems Engineering, 22, 4, 385-400, (2013)
[148] Di Pillo, G.; Lucidi, S.; Rinaldi, F., A derivative-free algorithm for constrained global optimization based on exact penalty functions, Journal of Optimization Theory and Applications, (2013) · Zbl 1259.90099
[149] Ding, Y.; Ge, D.; Wolkowicz, H., On equivalence of semidefinite relaxations for quadratic matrix programming, Mathematics of Operations Research, 36, 1, 88-104, (2011) · Zbl 1218.90149
[150] Dipama, J.; Teyssedou, A.; Sorin, M., Synthesis of heat exchanger networks using genetic algorithms, Applied Thermal Engineering, 28, 14-15, 1763-1773, (2008)
[151] Domes, F., Gloptlab - a configurable framework for the rigorous global solution of quadratic constraint satisfaction problems, Optimization Methods and Software, 24, 727-747, (2009) · Zbl 1180.90217
[152] Domes, F.; Neumaier, A., Constraint propagation on quadratic constraints, Constraints, 15, 3, 404-429, (2010) · Zbl 1208.68200
[153] Domes, F.; Neumaier, A., Rigorous enclosures of ellipsoids and directed Cholesky factorizations, SIAM Journal on Matrix Analysis and Applications, 32, 262-285, (2011) · Zbl 1242.90152
[154] Domes, F.; Neumaier, A., Constraint aggregation for rigorous global optimization, Mathematical Programming, (2014)
[155] Domschke, P.; Geissler, B.; Kolb, O.; Lang, J.; Martin, A.; Morsi, A., Combination of nonlinear and linear optimization of transient gas networks, INFORMS Journal on Computing, 23, 4, 605-617, (2011) · Zbl 1243.90030
[156] Dorneich, M. C.; Sahinidis, N. V., Global optimization algorithms for chip layout and compaction, Engineering Optimization, 25, 131-154, (1995)
[157] Du, K.; Kearfott, R. B., The cluster problem in multivariate global optimization, Journal of Global Optimization, 5, 3, 253-265, (1994) · Zbl 0824.90121
[158] Duran, M. A.; Grossmann, I. E., A mixed-integer nonlinear programming algorithm for process systems synthesis, AIChE Journal, 32, 4, 592-606, (1986)
[159] Duran, M. A.; Grossmann, I. E., An outer-approximation algorithm for a class of mixed-integer nonlinear programs, Mathematical Programming, 36, 307-339, (1986) · Zbl 0619.90052
[160] Egea, J. A.; Martí, R.; Banga, J. R., An evolutionary method for complex-process optimization, Computers & Operations Research, 37, 2, 315-324, (2010) · Zbl 1175.90427
[161] Egea, J. A.; Rodrigues-Fernandez, M. P.; Banga, J. R.; Marti, R., Scatter search for chemical and bio-process optimization, Journal of Global Optimization, 37, 3, 481-503, (2007) · Zbl 1108.92001
[162] Egea, J. A.; Vries, D.; Alonso, A. A.; Banga, J. R., Global optimization for integrated design and control of computationally expensive process models, Industrial & Engineering Chemistry Research, 46, 26, 9148-9157, (2007)
[163] Eldred, M. S., Adams, B. M., Gay, D. M., Swiller, L. P., Haskell, K., Bohnhoff, W. J., Eddy, J. P., Hart, W. E., Watson, J. P., Hough, P. D. Kolda, T. G. (2008). DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification and sensitivity analysis. Available at: http://dakota.sandia.gov/docs/dakota/4.2/Developers4.2.pdf.
[164] Engelhart, M.; Funke, J.; Sager, S., A decomposition approach for a new test-scenario in complex problem solving, Journal of Computer Science, 4, 4, 245-254, (2013)
[165] Escobar, M. Grossmann, I. E. (2010). Mixed-integer nonlinear programming models for optimal simultaneous synthesis of heat exchangers network. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=93.
[166] Espinet, A.; Shoemaker, C.; Doughty, C., Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data, Water Resources Research, 49, 7, 4442-4464, (2013)
[167] Fahmi, I.; Cremaschi, S., Process synthesis of biodiesel production plant using artificial neural networks as the surrogate models, Computers & Chemical Engineering, 46, 105-123, (2012)
[168] Faria, D. C.; Bagajewicz, M. J., A new approach for global optimization of a class of MINLP problems with applications to water management and pooling problems, AIChE Journal, 58, 8, 2320-2335, (2012)
[169] Fasano, G.; Liuzzi, G.; Lucidi, S.; Rinaldi, F., A linesearch-based derivative-free approach for nonsmooth constrained optimization, SIAM Journal on Optimization, 24, 3, 959-992, (2014) · Zbl 1302.90207
[170] First, E. L.; Hasan, M. M.F.; Floudas, C. A., Discovery of novel zeolites for natural gas purification through combined material screening and process optimization, AIChE Journal, 60, 5, 1767-1785, (2014)
[171] Flores-Tlacuahuac, A. Grossmann, I. E. (2009). Simultaneous cyclic scheduling and control of a multiproduct CSTR. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=71.
[172] Floudas, C. A., Nonlinear and mixed-integer optimization: Fundamentals and applications, (1995), Oxford University Press New York, NY · Zbl 0886.90106
[173] Floudas, C. A., Deterministic global optimization : Theory, methods and applications, Nonconvex Optimization and Its Applications, (2000), Kluwer Academic Publishers Dordrecht, Netherlands
[174] Floudas, C. A.; Aggarwal, A., A decomposition strategy for global optimum search in the pooling problem, ORSA Journal on Computing, 2, 225-235, (1990) · Zbl 0755.90091
[175] Floudas, C. A.; Akrotirianakis, I. G.; Caratzoulas, S.; Meyer, C. A.; Kallrath, J., Global optimization in the 21st century: advances and challenges., Computers & Chemical Engineering, 29, 1185-1202, (2005)
[176] Floudas, C. A.; Anastasiadis, S. H., Synthesis of distillation sequences with several multicomponent feed and product streams, Chemical Engineering Science, 43, 9, 2407-2419, (1988)
[177] Floudas, C. A.; Elia, J. A.; Baliban, R. C., Hybrid and single feedstock energy processes for liquid transportation fuels: A critical review, Computers & Chemical Engineering, 41, 24-51, (2012)
[178] Floudas, C. A.; Gounaris, C. E., A review of recent advances in global optimization, Journal of Global Optimization, 45, 1, 3-38, (2009) · Zbl 1180.90245
[179] Floudas, C. A.; Grossmann, I. E., Synthesis of flexible heat-exchanger networks with uncertain flowrates and temperatures, Computers & Chemical Engineering, 11, 4, 319-336, (1987)
[180] (Floudas, C. A.; Pardalos, P. M., (1992), Princeton University Press Princeton, New Jersey)
[181] Floudas, C. A.; Pardalos, P. M., State-of-the-art in global optimization - computational methods and applications - preface, Journal of Global Optimization, 7, 2, 113, (1995)
[182] (Floudas, C. A.; Pardalos, P. M., (1996), Kluwer Academic Publishers)
[183] (Floudas, C. A.; Pardalos, P. M., (2000), Nonconvex Optimization and Its Applications. Kluwer Academic Publishers)
[184] (Floudas, C. A.; Pardalos, P. M., (2004), Nonconvex Optimization and Its Applications Kluwer Academic Publishers)
[185] Floudas, C. A.; Pardalos, P. M.; Adjiman, C. S.; Esposito, W. R.; Gümüs, Z. H.; Harding, S. T.; Schweiger, C. A., Handbook of test problems in local and global optimization, (1999), Kluwer Academic Publishers · Zbl 0943.90001
[186] Floudas, C. A.; Paules, G. E., A mixed-integer nonlinear programming formulation for the synthesis of heat-integrated distillation sequences, Computers & Chemical Engineering, 12, 6, 531-546, (1988)
[187] Floudas, C. A.; Visweswaran, V., A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. theory, Computers & Chemical Engineering, 14, 12, 1397-1417, (1990)
[188] Floudas, C. A.; Visweswaran, V., Primal-relaxed dual global optimization approach, Journal of Optimization Theory and Applications, 78, 2, 187-225, (1993) · Zbl 0796.90056
[189] Forrester, A. I.J.; Jones, D. R., Global optimization of deceptive functions with sparse sampling, AIAA/ISSMO multidisciplinary analysis and optimization conference, (2008), American Institute of Aeronautics and Astronautics Victoria, British Columbia Canada
[190] Forrester, A. I.J.; Keane, A. J., Recent advances in surrogate-based optimization, Progress in Aerospace Sciences, 45, 1, 50-79, (2009)
[191] Forrester, A. I.J.; Sobester, A.; Keane, A. J., Engineering design via surrogate modelling - A practical guide, (2008), John Wiley & Sons
[192] Fourer, R.; Gay, D. M.; Kernighan, B. W., The AMPL book. AMPL: A modeling language for mathematical programming, (2002), Duxbury Press, Brooks/Cole Publishing Company
[193] Fowler, K. R.; Reese, J. P.; Kees, C. E.; Dennis, J. E.; Kelley, C. T., Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems, Water Resources, 31, 743-757, (2008)
[194] Fügenschuh, A.; Geissler, B.; Gollmer, R.; Hayn, C.; Henrion, R.; Hiller, B.; Willert, B. M., Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets, Energy Systems, 5, 3, 449-473, (2014)
[195] Fügenschuh, A.; Homfeld, H.; Schülldorf, H.; Vigerske, S., Mixed-integer nonlinear problems in transportation applications, (Rodrigues, H., Proceedings of the 2nd international conference on engineering optimization, (2010))
[196] Gablonsky, J. M., Modifications of the DIRECT algorithm, (2001), North Carolina State University, (Ph.D. in Mathematics) · Zbl 1039.90049
[197] Garcia-Palomares, U. M.; Costa-Montenegro, E.; Asorey-Cacheda, R.; Gonzalez-Castano, F. J., Adapting derivative free optimization methods to engineering models with discrete variables, Optimization and Engineering, 13, 4, 579-594, (2012) · Zbl 1293.65092
[198] Garcia-Palomares, U. M.; Garcia-Urrea, I. J.; Rodriguez-Hernandez, P. S., On sequential and parallel non-monotone derivative-free algorithms for box constrained optimization, Optimization Methods and Software, 28, 6, 1233-1261, (2013) · Zbl 1278.65088
[199] Garcia-Palomares, U. M.; Gonzalez-Castano, F. J.; Burguillo-Rial, J. C., A combined global and local search (CGLS) approach to global optimization, Journal of Global Optimization, 34, 3, 409-426, (2006) · Zbl 1149.90426
[200] Gassner, M.; Maréchal, F., Methodology for the optimal thermo-economic, multi-objective design of thermochemical fuel production from biomass, Computers & Chemical Engineering, 33, 3, 769-781, (2009)
[201] Gatzke, E. P.; Tolsma, J. E.; Barton, P. I., Construction of convex relaxations using automated code generation techniques, Optimization and Engineering, 3, 305-326, (2002) · Zbl 1035.90063
[202] Gau, C. Y.; Schrage, L. E., Implementation and testing of a branch-and-bound based method for deterministic global optimization: operations research applications, (Floudas, C. A.; Pardalos, P. M., Frontiers in global optimization, (2003), Kluwer Academic Publishers), 145-164 · Zbl 1165.90687
[203] Geissler, B.; Morsi, A.; Schewe, L., A new algorithm for MINLP applied to gas transport energy cost minimization, (Jünger, M.; Reinelt, G., Facets of combinatorial optimization, (2013), Springer Berlin Heidelberg), 321-353 · Zbl 1317.90209
[204] Gentilini, I.; Margot, F.; Shimada, K., The travelling salesman problem with neighbourhoods: MINLP solution, Optimization Methods and Software, 28, 2, 364-378, (2013) · Zbl 1270.90055
[205] Geoffrion, A. M., Elements of large-scale mathematical programming .1. concepts, Management Science Series A-Theory, 16, 11, 652-675, (1970) · Zbl 0209.22801
[206] Gilmore, P.; Kelley, C., An implicit filtering algorithm for optimization of functions with many local minima, SIAM Journal on Optimization, 5, 2, 269-285, (1995) · Zbl 0828.65064
[207] Gleixner, A. M.; Held, H.; Huang, W.; Vigerske, S., Towards globally optimal operation of water supply networks, Numerical Algebra, Control and Optimization, 2, 4, 695-711, (2012) · Zbl 1269.90083
[208] Gleixner, A. M.; Weltge, S., Learning and propagating Lagrangian variable bounds for mixed-integer nonlinear programming, (Gomes, C.; Sellmann, M., Integration of ai and or techniques in constraint programming for combinatorial optimization problems, Lecture Notes in Computer Science, Vol. 7874, (2013), Springer Berlin Heidelberg), 355-361 · Zbl 1382.90063
[209] Gopalakrishnan, A. Biegler, L. (2011). MINLP and MPCC formulations for the cascading tanks problem. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=140.
[210] Gounaris, C. E.; First, E. L.; Floudas, C. A., Estimation of diffusion anisotropy in microporous crystalline materials and optimization of crystal orientation in membranes, Journal of Chemical Physics, 139, 12, 124703, (2013)
[211] Gounaris, C. E.; Floudas, C. A., Convexity of products of univariate functions and convexification transformations for geometric programming, Journal of Optimization Theory and Applications, 138, 407-427, (2008) · Zbl 1163.90017
[212] Gounaris, C. E.; Floudas, C. A., Tight convex underestimators for \(\mathcal{C}^2\)-continuous problems: I. univariate functions, Journal of Global Optimization, 42, 1, 51-67, (2008) · Zbl 1173.90503
[213] Gounaris, C. E.; Floudas, C. A., Tight convex underestimators for \(\mathcal{C}^2\)-continuous problems: II. multivariate functions, Journal of Global Optimization, 42, 1, 69-89, (2008) · Zbl 1170.90459
[214] Gounaris, C. E.; Misener, R.; Floudas, C. A., Computational comparison of piecewise-linear relaxations for pooling problems, Industrial & Engineering Chemistry Research, 48, 12, 5742-5766, (2009)
[215] Graciano, J. E.A.; Roux, G. A.C. L., Improvements in surrogate models for process synthesis. application to water network system design, Computers & Chemical Engineering, 59, 197-210, (2013)
[216] Granvilliers, L.; Benhamou, F., Algorithm 852: realpaver: an interval solver using constraint satisfaction techniques, ACM Transactions on Mathematical Software, 32, 1, 138-156, (2006) · Zbl 1346.65020
[217] Gratton, S.; Toint, P.; Tröltzsch, A., An active-set trust-region method for derivative-free nonlinear bound-constrained optimization, Optimization Methods and Software, 26, 4-5, 873-894, (2011) · Zbl 1229.90138
[218] Gratton, S.; Vicente, L., A merit function approach for direct search, SIAM Journal on Optimization, 24, 4, 1980-1998, (2014) · Zbl 1318.90077
[219] Gray, G. A.; Kolda, T. G.; Sale, K.; Young, M. M., Optimizing an empirical scoring function for transmembrane protein structure determination, INFORMS Journal on Computing, 16, 4, 406-418, (2004) · Zbl 1239.90115
[220] Griffin, J. D.; Kolda, T. G., Asynchronous parallel hybrid optimization combining DIRECT and GSS, Optimization Methods and Software, 25, 5, 797-817, (2010) · Zbl 1198.90397
[221] Gross, B.; Roosen, P., Total process optimization in chemical engineering with evolutionary algorithms, Computers & Chemical Engineering, 22, 1, S229-S236, (1998)
[222] Grossmann, I. E., Advances in mathematical programming models for enterprise-wide optimization, Computers & Chemical Engineering, 47, 2-18, (2012)
[223] Grossmann, I. E.; Biegler, L. T., Part II. future perspective on optimization, Computers & Chemical Engineering, 28, 8, 1193-1218, (2004)
[224] Grossmann, I. E.; Guillén-Gosálbez, G., Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes, Computers & Chemical Engineering, 34, 9, 1365-1376, (2010)
[225] Grossmann, I. E.; Sargent, R. W.H., Optimum design of multipurpose chemical plants, Industrial & Engineering Chemistry Process Design and Development, 18, 2, 343-348, (1979)
[226] Guillén-Gosálbez, G. Pozo, C. (2010). Optimization of metabolic networks in biotechnology. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=81.
[227] Guillén-Gosálbez, G.; Sorribas, A., Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses, BMC Bioinformatics, 10, 386, (2009)
[228] Gupte, A.; Ahmed, S.; Cheon, M.; Dey, S., Solving mixed integer bilinear problems using MILP formulations, SIAM Journal on Optimization, 23, 2, 721-744, (2013) · Zbl 1300.90021
[229] Guzman, Y. A.; Hasan, M. M.F.; Floudas, C. A., Computational comparison of convex underestimators for use in a branch-and-bound global optimization framework, (Rassias, T. M.; Floudas, C. A.; Butenko, S., Optimization in science and engineering, (2014), Springer New York), 229-246 · Zbl 1321.90154
[230] Hager, W.; Phan, D., An ellipsoidal branch and bound algorithm for global optimization, SIAM Journal on Optimization, 20, 2, 740-758, (2009) · Zbl 1198.90318
[231] Han, J.; Kokkolaras, M.; Papalambros, P. Y., Optimal design of hybrid fuel cell vehicles, Journal of Fuel Cell Science and Technology, 5, 4, (2008)
[232] Hare, W.; Nutini, J., A derivative-free approximate gradient sampling algorithm for finite minimax problems, Computational Optimization and Applications, 56, 1, 1-38, (2013) · Zbl 1300.90064
[233] Harjunkoski, I.; Maravelias, C. T.; Bongers, P.; Castro, P. M.; Engell, S.; Grossmann, I. E.; Wassick, J., Scope for industrial applications of production scheduling models and solution methods, Computers & Chemical Engineering, 62, 161-193, (2014)
[234] Harjunkoski, I.; Westerlund, T.; Isaksson, J.; Skrifvars, H., Different formulations for solving trim loss problems in a paper-converting mill with ILP, Computers & Chemical Engineering, 20, Supplement 1, S121-S126, (1996)
[235] Harjunkoski, I.; Westerlund, T.; Pörn, R.; Skrifvars, H., Different transformations for solving non-convex trim-loss problems by MINLP, European Journal of Operational Research, 105, 3, 594-603, (1998) · Zbl 0955.90095
[236] Hasan, M. M.F.; Baliban, R. C.; Elia, J. A.; Floudas, C. A., Modeling, simulation, and optimization of postcombustion CO2 capture for variable feed concentration and flow rate. 2. pressure swing adsorption and vacuum swing adsorption processes, Industrial & Engineering Chemistry Research, 51, 48, 15665-15682, (2012)
[237] Hasan, M. M.F.; Boukouvala, F.; First, E. L.; Floudas, C. A., Nationwide, regional, and statewide CO2 capture, utilization, and sequestration supply chain network optimization, Industrial & Engineering Chemistry Research, 53, 18, 7489-7506, (2014)
[238] Hasan, M. M.F.; First, E. L.; Boukouvala, F.; Floudas, C. A., A multi-scale framework for CO2 capture, utilization and sequestration: CCUS and CCU, Computers and Chemical Engineering, 81, 2-21, (2015)
[239] Hasan, M. M.F.; First, E. L.; Floudas, C. A., Cost-effective CO2 capture based on in silico screening of zeolites and process optimization, Physical Chemistry Chemical Physics, 15, 17601-17618, (2013)
[240] Hasan, M. M.F.; Karimi, I. A., Piecewise linear relaxation of bilinear programs using bivariate partitioning, AIChE Journal, 56, 7, 1880-1893, (2010)
[241] Hasan, M. M.F.; Karimi, I. A.; Avison, C. M., Preliminary synthesis of fuel gas networks to conserve energy and preserve the environment, Industrial & Engineering Chemistry Research, 50, 12, 7414-7427, (2011)
[242] Hayes, R. E.; Bertrand, F. H.; Audet, C.; Kolaczkowski, S. T., Catalytic combustion kinetics: using a direct search algorithm to evaluate kinetic parameters from light-off curves, The Canadian Journal of Chemical Engineering, 81, 6, 1192-1199, (2003)
[243] Hemker, T.; Werner, C., DIRECT using local search on surrogates, Pacific Journal of Optimization, 7, 3, 443-466, (2011) · Zbl 1228.90079
[244] Hemmecke, R.; Köppe, M.; Lee, J.; Weismantel, R., Nonlinear integer programming, (Jünger, M.; Liebling, T. M.; Naddef, D.; Nemhauser, G. L.; Pulleyblank, W. R.; Reinelt, G.; Rinaldi, G.; Wolsey, L. A., 50 years of integer programming 1958-2008, (2010), Springer Berlin Heidelberg), 561-618 · Zbl 1187.90270
[245] Henao, C. A.; Maravelias, C. T., Surrogate-based superstructure optimization framework, AIChE Journal, 57, 5, 1216-1232, (2011)
[246] Henrion, D.; Lasserre, J.-B., Gloptipoly: global optimization over polynomials with Matlab and sedumi, ACM Transactions on Mathematical Software, 29, 2, 165-194, (2003) · Zbl 1070.65549
[247] Henrion, D.; Lasserre, J. B.; Löfberg, J., Gloptipoly 3: moments, optimization and semidefinite programming, Optimization Methods and Software, 24, 4-5, 761-779, (2009) · Zbl 1178.90277
[248] Hifi, M.; M’Hallah, R., A literature review on circle and sphere packing problems: models and methodologies, Advances in Operations Research, 2009, 22, (2009) · Zbl 1198.90337
[249] Hladík, M., On the efficient Gerschgorin inclusion usage in the global optimization αBB method, Journal of Global Optimization, (2014)
[250] Hoai An, L. T., An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints, Mathematical Programming, 87, 401-426, (2000) · Zbl 0952.90031
[251] Holmström, K., Göran, A. O. Edvall, M. M.(2008a). Users guide for TOMLAB CGO. Available at: http://tomopt.com/docs/TOMLAB_CGO.pdf.
[252] Holmström, K.; Quttineh, N.-H.; Edvall, M. M., An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization, Optimization and Engineering, 9, 4, 311-339, (2008) · Zbl 1400.90226
[253] Hooke, R.; Jeeves, T. A., Direct search solution of numerical and statistical problems, Journal of the ACM, 8, 2, 212-229, (1961) · Zbl 0111.12501
[254] Horst, R.; Tuy, H., Global optimization: Deterministic approaches, (1996), Springer · Zbl 0867.90105
[255] Huyer, W.; Neumaier, A., Global optimization by multilevel coordinate search, Journal of Global Optimization, 14, 4, 331-355, (1999) · Zbl 0956.90045
[256] Huyer, W.; Neumaier, A., SNOBFIT - stable noisy optimization by branch and fit, ACM Transactions on Mathematical Software, 35, 2, (2008)
[257] Jach, M.; Michaels, D.; Weismantel, R., The convex envelope of (n-1) convex functions, The SIAM Journal on Optimization, 19, 3, 1451-1466, (2008) · Zbl 1176.90467
[258] Jakobsson, S.; Patriksson, M.; Rudholm, J.; Wojciechowski, A., A method for simulation based optimization using radial basis functions, Optimization and Engineering, 11, 4, 501-532, (2010) · Zbl 1243.65068
[259] Jansson, N.; Wakeman, W. D.; Manson, J. A.E., Optimization of hybrid thermoplastic composite structures using surrogate models and genetic algorithms, Composite Structures, 80, 1, 21-31, (2007)
[260] Jeżowski, J., Review of water network design methods with literature annotations, Industrial & Engineering Chemistry Research, 49, 10, 4475-4516, (2010)
[261] Jones, D. R., A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, 21, 4, 345-383, (2001) · Zbl 1172.90492
[262] Jones, D. R. (2008). MOPTA 2008 benchmark. Available at: http://anjos.mgi.polymtl.ca/MOPTA2008Benchmark.html.
[263] Jones, D. R.; Perttunen, C. D.; Stuckman, B. E., Lipschitzian optimization without the Lipschitz constant, Journal of Optimization Theory and Applications, 79, 1, 157-181, (1993) · Zbl 0796.49032
[264] Jones, D. R.; Schonlau, M.; Welch, W. J., Efficient global optimization of expensive black-box functions, Journal of Global Optimization, 13, 4, 455-492, (1998) · Zbl 0917.90270
[265] Kallrath, J., Exact computation of global minima of a nonconvex portfolio optimization problem, (Floudas, C. A.; Pardalos, P. M., Frontiers in global optimization, (2003), Kluwer Academic Publishers), 237-254 · Zbl 1176.90468
[266] Kallrath, J., Cutting circles and polygons from area-minimizing rectangles, Journal of Global Optimization, 43, 299-328, (2009) · Zbl 1169.90434
[267] Kallrath, J.; Rebennack, S., Cutting ellipses from area-minimizing rectangles, Journal of Global Optimization, 59, 2-3, 405-437, (2014) · Zbl 1301.90073
[268] Karuppiah, R.; Grossmann, I. E., Global optimization for the synthesis of integrated water systems in chemical processes, Computers & Chemical Engineering, 30, 650-673, (2006)
[269] Kelley, C., Implicit filtering, (2011), Society for Industrial and Applied Mathematics · Zbl 1246.68017
[270] Khajavirad, A.; Sahinidis, N. V., Convex envelopes of products of convex and component-wise concave functions, Journal of Global Optimization, 52, 391-409, (2012) · Zbl 1268.90052
[271] Khajavirad, A.; Sahinidis, N. V., Convex envelopes generated from finitely many compact convex sets, Mathematical Programming, 137, 1-2, 371-408, (2013) · Zbl 1284.90055
[272] Khor, C. S.; Chachuat, B.; Shah, N., Fixed-flowrate total water network synthesis under uncertainty with risk management, Journal of Cleaner Production, 77, 0, 79-93, (2014)
[273] Kleijnen, J. P.C.; van Beers, W.; van Nieuwenhuyse, I., Constrained optimization in expensive simulation: novel approach, European Journal of Operational Research, 202, 1, 164-174, (2010) · Zbl 1189.90156
[274] Kleniati, P.; Parpas, P.; Rustem, B., Decomposition-based method for sparse semidefinite relaxations of polynomial optimization problems, Journal of Optimization Theory and Applications, 145, 2, 289-310, (2010) · Zbl 1197.90332
[275] Kleniati, P.-M.; Adjiman, C. S., Branch-and-sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. part I: theoretical development, Journal of Global Optimization, 60, 3, 425-458, (2014) · Zbl 1310.90093
[276] Kleniati, P.-M.; Adjiman, C. S., Branch-and-sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. part II: convergence analysis and numerical results, Journal of Global Optimization, 60, 3, 425-458, (2014) · Zbl 1310.90093
[277] Klepeis, J. L.; Floudas, C. A.; Morikis, D.; Tsokos, C. G.; Lambris, J. D., Design of peptide analogues with improved activity using a novel de novo protein design approach, Industrial & Engineering Chemistry Research, 43, 14, 3817-3826, (2004)
[278] Klepeis, J. L.; Pieja, M. J.; Floudas, C. A., Hybrid global optimization algorithms for protein structure prediction: alternating hybrids, Biophysical Journal, 84, 2, 869-882, (2003) · Zbl 1196.90134
[279] Klepeis, J. L.; Pieja, M. J.; Floudas, C. A., A new class of hybrid global optimization algorithms for peptide structure prediction: integrated hybrids, Computer Physics Communications, 151, 2, 121-140, (2003) · Zbl 1196.90134
[280] Kocis, G. R.; Grossmann, I. E., Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis, Industrial & Engineering Chemistry Research, 27, 8, 1407-1421, (1988)
[281] Kokkolaras, M.; Audet, C.; Dennis, J. E., Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system, Optimization and Engineering, 2, 1, 5-29, (2001) · Zbl 1078.90595
[282] Kokossis, A. C.; Floudas, C. A., Synthesis of isothermal reactor-separator-recycle systems, Chemical Engineering Science, 46, 5 - 6, 1361-1383, (1991)
[283] Kokossis, A. C.; Floudas, C. A., Optimization of complex reactor networks-II. nonisothermal operation., Chemical Engineering Science, 49, 7, 1037-1051, (1994)
[284] Kolda, T. G.; Lewis, R. M.; Torczon, V., Optimization by direct search: new perspectives on some classical and modern methods, SIAM Review, 45, 3, 385-482, (2003) · Zbl 1059.90146
[285] Kolda, T. G.; Lewis, R. M.; Torczon, V., Stationarity results for generating set search for linearly constrained optimization, SIAM Journal on Optimization, 17, 4, 943-968, (2006) · Zbl 1126.90076
[286] Kolodziej, S. P.; Castro, P. M.; Grossmann, I. E., Global optimization of bilinear programs with a multiparametric disaggregation technique, Journal of Global Optimization, 57, 4, 1039-1063, (2013) · Zbl 1282.90137
[287] Kolodziej, S. P.; Grossmann, I. E.; Furman, K. C.; Sawaya, N. W., A discretization-based approach for the optimization of the multiperiod blend scheduling problem, Computers & Chemical Engineering, 53, 122-142, (2013)
[288] (Koziel, V.; Yang, X. S., Vol. 356, (2011), Studies in Computational Intelligence. Springer)
[289] Laguna, M.; Gortźar, F.; Gallego, M.; Duarte, A.; Martí, R., A black-box scatter search for optimization problems with integer variables, Journal of Global Optimization, 58, 3, 497-516, (2014) · Zbl 1305.90304
[290] Lasserre, J., Convergent SDP relaxations in polynomial optimization with sparsity, SIAM Journal on Optimization, 17, 3, 822-843, (2006) · Zbl 1119.90036
[291] Le Digabel, S., Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm, ACM Transactions on Mathematical Software, 37, 4, 1-15, (2011) · Zbl 1365.65172
[292] Le Thi, H. A.; Vaz, A. I.F.; Vicente, L. N., Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization, TOP, 20, 1, 190-214, (2012) · Zbl 1267.90110
[293] Lebbah, Y.; Michel, C.; Rueher, M., A rigorous global filtering algorithm for quadratic constraints, Constraints, 10, 1, 47-65, (2005) · Zbl 1066.90090
[294] Lee, H.; Pinto, J. M.; Grossmann, I. E.; Park, S., Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management, Industrial & Engineering Chemistry Research, 35, 5, 1630-1641, (1996)
[295] (Lee, J.; Leyffer, S., (2012), The IMA Volumes in Mathematics and its Applications. Springer)
[296] Lewis, R.; Shepherd, A.; Torczon, V., Implementing generating set search methods for linearly constrained minimization, SIAM Journal on Scientific Computing, 29, 6, 2507-2530, (2007) · Zbl 1166.90368
[297] Lewis, R.; Torczon, V., Pattern search algorithms for bound constrained minimization, SIAM Journal on Optimization, 9, 4, 1082-1099, (1999) · Zbl 1031.90047
[298] Lewis, R.; Torczon, V., Pattern search methods for linearly constrained minimization, SIAM Journal on Optimization, 10, 3, 917-941, (2000) · Zbl 1031.90048
[299] Leyffer, S.; Linderoth, J.; Luedtke, J.; Miller, A.; Munson, T., Applications and algorithms for mixed integer nonlinear programming, Journal of Physics: Conference Series, 180, 1, 012014, (2009)
[300] Li, J.; Li, A.; Karimi, I. A.; Srinivasan, R., Improving the robustness and efficiency of crude scheduling algorithms, AIChE Journal, 53, 10, 2659-2680, (2007)
[301] Li, J.; Misener, R.; Floudas, C. A., Continuous-time modeling and global optimization approach for scheduling of crude oil operations, AIChE Journal, 58, 1, 205-226, (2012)
[302] Li, J.; Misener, R.; Floudas, C. A., Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization, AIChE Journal, 58, 8, 2373-2396, (2012)
[303] Li, X.; Armagan, E.; Tomasgard, A.; Barton, P. I., Stochastic pooling problem for natural gas production network design and operation under uncertainty, AIChE Journal, 57, 8, 2120-2135, (2011)
[304] Li, X.; Tomasgard, A.; Barton, P. I., Decomposition strategy for the stochastic pooling problem, Journal of Global Optimization, 54, 4, 765-790, (2012) · Zbl 1282.90141
[305] Liberti, L., Reformulations in mathematical programming: automatic symmetry detection and exploitation, Mathematical Programming, 131, 1-2, 273-304, (2012) · Zbl 1235.90103
[306] Liberti, L.; Cafieri, S.; Savourey, D., The reformulation-optimization software engine, Proceedings of the third international congress conference on mathematical software, ICMS’10, 303-314, (2010) · Zbl 1294.68160
[307] Liberti, L.; Cafieri, S.; Tarissan, F., Reformulations in mathematical programming: A computational approach, (Abraham, A.; Hassanien, A.-E.; Siarry, P.; Engelbrecht, A., Foundations of computational intelligence volume 3, Studies in Computational Intelligence, 203, (2009), Springer, Berlin), 153-234
[308] Liberti, L.; Lavor, C.; Maculan, N.; Nascimento, M., Reformulation in mathematical programming: an application to quantum chemistry, Discrete Applied Mathematics, 157, 6, 1309-1318, (2009) · Zbl 1173.90494
[309] Liberti, L.; Maculan, N., Global optimization: From theory to implementation, Nonconvex Optimization and its Applications, (2006), Springer
[310] Liberti, L.; Mladenović, N.; Nannicini, G., A recipe for finding good solutions to minlps, Mathematical Programming Computation, 3, 349-390, (2011) · Zbl 1276.90041
[311] Liberti, L.; Pantelides, C. C., Convex envelopes of monomials of odd degree, Journal of Global Optimization, 25, 157-168, (2003) · Zbl 1030.90117
[312] Liberti, L.; Pantelides, C. C., An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms, Journal of Global Optimization, 36, 2, 161-189, (2006) · Zbl 1131.90045
[313] Lima, R. M.; Francois, G.; Srinivasan, B.; Salcedo, R. L., Dynamic optimization of batch emulsion polymerization using MSIMPSA, a simulated- annealing-based algorithm, Industrial & Engineering Chemistry Research, 43, 24, 7796-7806, (2004)
[314] Lin, X.; Floudas, C. A., Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation, Computers & Chemical Engineering, 25, 4-6, 665-674, (2001)
[315] Lin, X.; Floudas, C. A.; Kallrath, J., Global solution approach for a nonconvex MINLP problem in product portfolio optimization, Journal of Global Optimization, 32, 417-431, (2005) · Zbl 1098.90098
[316] Lin, Y.; Schrage, L., The global solver in the LINDO API, Optimization Methods and Software, 24, 4-5, 657-668, (2009) · Zbl 1177.90325
[317] Linderoth, J., A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs, Mathematical Programming, 103, 2, 251-282, (2005) · Zbl 1099.90039
[318] Liu, W. B.; Floudas, C. A., A remark on the GOP algorithm for global optimization, Journal of Global Optimization, 3, 519-521, (1993) · Zbl 0785.90089
[319] Liuzzi, G.; Lucidi, S., A derivative-free algorithm for inequality constrained nonlinear programming via smoothing of an l- ∞ penalty function, SIAM Journal on Optimization, 20, 1, 1-29, (2009) · Zbl 1187.65065
[320] Liuzzi, G.; Lucidi, S.; Piccialli, V., Exploiting derivative-free local searches in direct-type algorithms for global optimization, Computational Optimization and Applications, 1-27, (2015)
[321] Liuzzi, G.; Lucidi, S.; Rinaldi, F., Derivative-free methods for bound constrained mixed-integer optimization, Computational Optimization and Applications, 53, 2, 505-526, (2012) · Zbl 1257.90058
[322] Liuzzi, G.; Lucidi, S.; Rinaldi, F., Derivative-free methods for mixed-integer constrained optimization problems, Journal of Optimization Theory and Applications, 164, 3, 933-965, (2015) · Zbl 1321.90087
[323] Liuzzi, G.; Lucidi, S.; Sciandrone, M., Sequential penalty derivative-free methods for nonlinear constrained optimization, The SIAM Journal on Optimization, 20, 5, 2614-2635, (2010) · Zbl 1223.65045
[324] Locatelli, M., Computing the value of the convex envelope of quadratic forms over polytopes through a semidefinite program, Operations Research Letters, 41, 4, 370-372, (2013) · Zbl 1286.90108
[325] Locatelli, M., A technique to derive the analytical form of convex envelopes for some bivariate functions, Journal of Global Optimization, 59, 2-3, 477-501, (2014) · Zbl 1326.90082
[326] Locatelli, M., Alternative branching rules for some nonconvex problems, Optimization Methods and Software, 30, 2, 365-378, (2015) · Zbl 1326.90066
[327] Locatelli, M.; Schoen, F., Global optimization: Theory, algorithms, and applications, 15, (2013), SIAM · Zbl 1286.90003
[328] Locatelli, M.; Schoen, F., On convex envelopes for bivariate functions over polytopes, Mathematical Programming, 144, 1-2, 65-91, (2014) · Zbl 1295.90055
[329] Loiola, E. M.; de Abreu, N. M.M.; Boaventura-Netto, P. O.; Hahn, P.; Querido, T., A survey for the quadratic assignment problem, European Journal of Operational Research, 176, 2, 657-690, (2007) · Zbl 1103.90058
[330] Lovász, L., Submodular functions and convexity, (Grö?tschel, M.; Kor, B., Mathematical programming: The state of the art, (1982), Springer), 235-257
[331] Lucidi, S.; Piccialli, V.; Sciandrone, M., An algorithm model for mixed variable programming, The SIAM Journal on Optimization, 15, 4, 1057-1084, (2005) · Zbl 1077.65064
[332] Lucidi, S.; Sciandrone, M., A derivative-free algorithm for bound constrained optimization, Computational Optimization and Applications, 21, 2, 119-142, (2002) · Zbl 0988.90033
[333] Luedtke, J.; Namazifar, M.; Linderoth, J., Some results on the strength of relaxations of multilinear functions, Mathematical Programming, 136, 2, 325-351, (2012) · Zbl 1286.90117
[334] Lundell, A.; Skjäl, A.; Westerlund, T., A reformulation framework for global optimization, Journal of Global Optimization, 57, 1, 115-141, (2013) · Zbl 1277.90102
[335] Lundell, A.; Westerlund, J.; Westerlund, T., Some transformation techniques with applications in global optimization, Journal of Global Optimization, 43, 391-405, (2009) · Zbl 1169.90453
[336] Lundell, A.; Westerlund, T., Convex underestimation strategies for signomial functions, Optimization Methods and Software, 24, 4-5, 505-522, (2009) · Zbl 1178.90278
[337] Lundell, A.; Westerlund, T., Global optimization of mixed-integer signomial programming problems, (Lee, J.; Leyffer, S., Mixed integer nonlinear programming, The IMA Volumes in Mathematics and its Applications, 154, (2012), Springer New York), 349-369 · Zbl 1242.90137
[338] Maleki, S.; Sawhney, R.; Farvaresh, H.; Sepehri, M. M., Energy efficient hybrid wired-cum-wireless sensor network design, Journal of Cleaner Production, 85, 0, 408-418, (2014)
[339] Maranas, C. D.; Androulakis, I. P.; Floudas, C. A.; Berger, A. J.; Mulvey, J. M., Solving long-term financial planning problems via global optimization, Journal of Economic Dynamics and Control, 21, 8-9, 1405-1425, (1997) · Zbl 0901.90016
[340] Maranas, C. D.; Floudas, C. A., A global optimization approach for lennard-Jones microclusters, Journal of Chemical Physics, 97, 10, 7667-7678, (1992)
[341] Maranas, C. D.; Floudas, C. A., Finding all solutions of nonlinearly constrained systems of equations, Journal of Global Optimization, 7, 2, 143-182, (1995) · Zbl 0841.90115
[342] Maranas, C. D.; Floudas, C. A., Global optimization in generalized geometric programming, Computers & Chemical Engineering, 21, 4, 351-369, (1997)
[343] March, A.; Willcox, K., Constrained multifidelity optimization using model calibration, Structural and Multidisciplinary Optimization, 46, 1, 93-109, (2012) · Zbl 1274.74286
[344] Marsden, A. L.; Feinstein, J. A.; Taylor, C. A., A computational framework for derivative-free optimization of cardiovascular geometries, Computer Methods in Applied Mechanics and Engineering, 197, 21-24, 1890-1905, (2008) · Zbl 1194.76296
[345] Marsden, A. L.; Wang, M.; Dennis, J. E.; Parviz, M., Optimal aerocoustic shape design using surrogate management framework, Optimization and Engineering, 5, 2, 235-262, (2004) · Zbl 1116.90417
[346] Marsden, A. L.; Wang, M.; Dennis, J. E.; Parviz, M., Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation, Journal of Fluid Mechanics, 572, 13-36, (2007) · Zbl 1145.76044
[347] Martelli, E.; Amaldi, E., PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems: brief review, novel algorithm and comparative evaluation, Computers & Chemical Engineering, 63, 108-139, (2014)
[348] Martelli, E.; Amaldi, E.; Consonni, S., Numerical optimization of heat recovery steam cycles: mathematical model, two-stage algorithm and applications, Computers & Chemical Engineering, 35, 12, 2799-2823, (2011)
[349] Martinez, J. M.; Sobral, F. N.C., Constrained derivative-free optimization on thin domains, Journal of Global Optimization, 56, 3, 1217-1232, (2013) · Zbl 1272.90091
[350] McCormick, G. P., Computability of global solutions to factorable nonconvex programs: part 1-convex underestimating problems, Mathematical Programming, 10, 1, 147-175, (1976) · Zbl 0349.90100
[351] McDonald, C. M.; Floudas, C. A., Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem, Journal of Global Optimization, 5, 3, 205-251, (1994) · Zbl 0820.90100
[352] McDonald, C. M.; Floudas, C. A., Global optimization for the phase and chemical equilibrium problem: application to the NRTL equation, Computers & Chemical Engineering, 19, 11, 1111-1139, (1995)
[353] McDonald, C. M.; Floudas, C. A., Global optimization for the phase stability problem, AIChE Journal, 41, 7, 1798-1814, (1995)
[354] McDonald, C. M.; Floudas, C. A., GLOPEQ: A new computational tool for the phase and chemical equilibrium problem, Computers & Chemical Engineering, 21, 1, 1-23, (1996)
[355] Meyer, C. A.; Floudas, C. A., Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes, (Floudas, C. A.; Pardalos, P. M., Frontiers in global optimization, (2003), Kluwer Academic Publishers), 327-352 · Zbl 1176.90469
[356] Meyer, C. A.; Floudas, C. A., Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes, Journal of Global Optimization, 29, 2, 125-155, (2004) · Zbl 1085.90047
[357] Meyer, C. A.; Floudas, C. A., Convex envelopes for edge-concave functions, Mathematical Programming, 103, 2, 207-224, (2005) · Zbl 1099.90045
[358] Meyer, C. A.; Floudas, C. A., Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: spline αBB underestimators, Journal of Global Optimization, 32, 2, 221-258, (2005) · Zbl 1080.90059
[359] Meyer, C. A.; Floudas, C. A., Global optimization of a combinatorially complex generalized pooling problem, AIChE Journal, 52, 3, 1027-1037, (2006)
[360] Meza, J. C.; Martinez, M. L., Direct search methods for the molecular conformation problem, Journal of Computational Chemistry, 15, 6, 627-632, (1994)
[361] Misener, R.; Floudas, C. A., Advances for the pooling problem: modeling, global optimization, and computational studies, Applied and Computational Mathematics, 8, 1, 3-22, (2009) · Zbl 1188.90287
[362] Misener, R.; Floudas, C. A., Global optimization of large-scale pooling problems: quadratically constrained MINLP models, Industrial & Engineering Chemistry Research, 49, 11, 5424-5438, (2010)
[363] Misener, R.; Floudas, C. A., Global optimization of mixed-integer models with quadratic and signomial functions: A review, Applied and Computational Mathematics, 11, 3, 317-336, (2012) · Zbl 1292.90239
[364] Misener, R.; Floudas, C. A., Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations, Mathematical Programming B, 136, 155-182, (2012) · Zbl 1257.90079
[365] Misener, R.; Floudas, C. A., Glomiqo: global mixed-integer quadratic optimizer, Journal of Global Optimization, 57, 1, 3-50, (2013) · Zbl 1272.90034
[366] Misener, R.; Floudas, C. A., ANTIGONE: algorithms for continuous integer global optimization of nonlinear equations, Journal of Global Optimization, 59, 2-3, 503-526, (2014) · Zbl 1301.90063
[367] Misener, R.; Floudas, C. A., A framework for globally optimizing mixed-integer signomial programs, Journal of Optimization Theory and Applications, 161, 905-932, (2014) · Zbl 1303.90074
[368] Misener, R.; Garí, M. F.; Rende, M.; Velliou, E.; Panoskaltsis, N.; Pistikopoulos, E. N.; Mantalaris, A., Global superstructure optimisation of red blood cell production in a parallelised hollow fibre bioreactor, Computers & Chemical Engineering, 71, 532-553, (2014)
[369] Misener, R.; Gounaris, C. E.; Floudas, C. A., Mathematical modeling and global optimization of large-scale extended pooling problems with the (EPA) complex emissions constraints, Computers & Chemical Engineering, 34, 9, 1432-1456, (2010)
[370] Misener, R.; Smadbeck, J. B.; Floudas, C. A., Dynamically-generated cutting planes for mixed-integer quadratically-constrained quadratic programs and their incorporation into glomiqo 2.0, Optimization Methods and Software, 30, 1, 215-249, (2014) · Zbl 1325.90071
[371] Misener, R.; Thompson, J. P.; Floudas, C. A., APOGEE: global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes, Computers & Chemical Engineering, 35, 5, 876-892, (2011)
[372] Mitsos, A.; Barton, P. I., A dual extremum principle in thermodynamics, AIChE Journal, 53, 8, 2131-2147, (2007)
[373] Mitsos, A.; Chachuat, B.; Barton, P. I., Mccormick-based relaxations of algorithms, SIAM Journal on Optimization, 20, 2, 573-601, (2009) · Zbl 1192.65083
[374] Moles, C. G.; Mendes, P.; Banga, J. R., Parameter estimation in biochemical pathways: A comparison of global optimization methods, Genome Research, 13, 2467-2474, (2003)
[375] Moré, J. J.; Wild, S. M., Benchmarking derivative-free optimization algorithms, SIAM Journal on Optimization, 91, 201-213, (2002)
[376] Morin, A.; Wahl, P. E.; Malnvik, M., Using evolutionary search to optimise the energy consumption for natural gas liquefaction, Chemical Engineering Research and Design, 89, 1, 2428-2441, (2011)
[377] Mouret, S. Grossmann, I. E. (2010). Crude-oil operations scheduling. Available from CyberInfrastructure for MINLP [A collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=117.
[378] Mouret, S.; Grossmann, I. E.; Pestiaux, P., A novel priority-slot based continuous-time formulation for crude-oil scheduling problems, Industrial & Engineering Chemistry Research, 48, 18, 8515-8528, (2009)
[379] Mouret, S.; Grossmann, I. E.; Pestiaux, P., A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling, Computers & Chemical Engineering, 35, 12, 2750-2766, (2011)
[380] Mugunthan, P.; Shoemaker, C. A.; Regis, R. G., Comparison of function approximation, heuristic, and derivative-based methods for automatic calibration of computationally expensive groundwater bioremediation models, Water Resources Research, 41, 11, W11427, (2005)
[381] Müller, J.; Shoemaker, C. A., Influence ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization methods, Journal of Global Optimization, 60, 2, 123-144, (2014) · Zbl 1312.90064
[382] Müller, J.; Shoemaker, C. A.; Piche, R., SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems, Computers & Operations Research, 40, 5, 1383-1400, (2013) · Zbl 1352.90067
[383] Nannicini, G.; Belotti, P., Rounding-based heuristics for nonconvex minlps, Mathematical Programming Computation, 4, 1, 1-31, (2012) · Zbl 1257.90059
[384] Nelder, J. A.; Mead, R., A simplex method for function minimization, Computer Journal, 7, 308-313, (1965) · Zbl 0229.65053
[385] Neumaier, A., Interval methods for systems of equations, Encyclopedia of Mathematics and its Applications, (1990), Cambridge University Press Cambridge
[386] Newby, E.; Ali, M. M., A trust-region-based derivative free algorithm for mixed integer programming, Computational Optimization and Applications, 60, 1, 199-229, (2014) · Zbl 1308.90112
[387] Nicosia, G.; Stracquadanio, G., Generalized pattern search algorithm for peptide structure prediction, Biophysical Journal, 95, 10, 4988-4999, (2008)
[388] Niknam, T.; Khodaei, A.; Fallahi, F., A new decomposition approach for the thermal unit commitment problem, Applied Energy, 86, 9, 1667-1674, (2009)
[389] Niziolek, A. M.; Onel, O.; Elia, J. A.; Baliban, R. C.; Xiao, X.; Floudas, C. A., Coal and biomass to liquid transportation fuels: process synthesis and global optimization strategies, Industrial & Engineering Chemistry Research, 53, 44, 17002-17025, (2014)
[390] Nowak, I., Relaxation and decomposition methods for mixed integer nonlinear programming, International series of numerical mathematics, (2005), Birkhäuser
[391] Nyberg, A., Grossmann, I. E. Westerlund, T. (2012). The optimal design of a three-echelon supply chain with inventories under uncertainty. Available from CyberInfrastructure for MINLP [www.minlp.org, a collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=157.
[392] Nyberg, A.; Grossmann, I. E.; Westerlund, T., An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands, AIChE Journal, 59, 1, 23-28, (2013)
[393] Oeuvray, R., Trust-region methods based on radial basis functions with application to biomedical imaging, (2005), Ecole Polytechnique Federale de Lausanne, (PhD in Mathematics)
[394] Oeuvray, R.; Bierlaire, M., A new derivative-free algorithm for the medical image registration problem, International Journal of Modeling and Simulation, 27, 2, 115-124, (2007)
[395] Onel, O.; Niziolek, A. M.; Hasan, M. M.F.; Floudas, C. A., Municipal solid waste to liquid transportation fuels part I: mathematical modeling of a municipal solid waste gasifier, Computers & Chemical Engineering, 71, 636-647, (2014)
[396] Ong, Y. S.; Nair, P. B.; Keane, A. J., Evolutionary optimization of computationally expensive problems via surrogate modeling, AIAA Journal, 41, 4, 687-696, (2003)
[397] Pal, L.; Csendes, T.; Markot, M. C.; Neumaier, A., Black box optimization benchmarking of the GLOBAL method, Evolutionary Computation, 20, 4, 609-639, (2012)
[398] Papadopoulos, A. I.; Linke, P., On the synthesis and optimization of liquid-liquid extraction processes using stochastic search methods, Computers & Chemical Engineering, 28, 11, 2391-2406, (2004)
[399] Papageorgiou, D. J.; Toriello, A.; Nemhauser, G. L.; Savelsbergh, M. W.P., Fixed-charge transportation with product blending, Transportation Science, 46, 2, 281-295, (2012)
[400] Pardalos, P. M., Global optimization algorithms for linearly constrained indefinite quadratic problems, Computers & Mathematics with Applications, 21, 6-7, 87-97, (1991) · Zbl 0733.90051
[401] Parpas, P.; Rustem, B., Global optimization of the scenario generation and portfolio selection problems, (Gavrilova, M.; Gervasi, O.; Kumar, V.; Tan, C.; Taniar, D.; Laganá, A.; Mun, Y.; Choo, H., Computational science and its applications - ICCSA 2006, Lecture Notes in Computer Science, 3982, (2006), Springer-Verlag), 908-917 · Zbl 1172.91324
[402] Parr, J. M.; Keane, A. J.; Forrester, A. I.J.; Holden, C. M.E., Infill sampling criteria for surrogate-based optimization with constraint handling, Engineering Optimization, 44, 10, 1147-1166, (2012)
[403] Parrilo, P. A., Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, 96, 293-320, (2003) · Zbl 1043.14018
[404] Pereira, F. E.; Jackson, G.; Galindo, A.; Adjiman, C. S., A duality-based optimisation approach for the reliable solution of (p, t) phase equilibrium in volume-composition space, Fluid Phase Equilibria, 299, 1, 1-23, (2010)
[405] Pfetsch, M. E.; Fügenschuh, A.; Geissler, B.; Geissler, N.; Gollmer, R.; Hiller, B.; Willert, B. M., Validation of nominations in gas network optimization: models, methods, and solutions, Optimization Methods and Software, 30, 1, 15-53, (2015) · Zbl 1325.90019
[406] Pham, V.; Laird, C.; El-Halwagi, M., Convex hull discretization approach to the global optimization of pooling problems, Industrial & Engineering Chemistry Research, 48, 1973-1979, (2009)
[407] Plantenga, T. D. (2009). HOPSPACK 2.0 User Manual. Available at: http://www.sandia.gov/hopspack/HopspackUserManual_2_0_2.pdf.
[408] Polisetty, P. K.; Gatzke, E. P.; Voit, E. O., Yield optimization of regulated metabolic systems using deterministic branch-and-reduce methods, Biotechnology and Bioengineering, 99, 5, 1154-1169, (2008)
[409] Ponce-Ortega, J. M.; El-Halwagi, M. M.; Jiménez-Gutiérrez, A., Global optimization for the synthesis of property-based recycle and reuse networks including environmental constraints, Computers & Chemical Engineering, 34, 3, 318-330, (2010)
[410] Powell, M. J.D., A direct search optimization method that models the objective and constraint functions by linear interpolation, Advances in optimization and numerical analysis, Mathematics and Its Applications, 275, 51-67, (1994), Springer Netherlands · Zbl 0826.90108
[411] Powell, M. J. D.. The BOBYQA algorithm for bound constrained optimization without derivatives, 2009. Available at: www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf.
[412] Powell, M. J. D.(2013a). COBYLA (constrained optimization by linear approximations). Available at: http://mat.uc.pt/ zhang/software.html#cobyla.
[413] Powell, M. J. D.(2013b). LINCOA (linearly constrained optimization algorithm). Available at: http://mat.uc.pt/ zhang/software.html#lincoa.
[414] Pozo, C.; Guillen-Gosalbez, G.; Sorribas, A.; Jimenez, L., A spatial branch-and-bound framework for the global optimization of kinetic models of metabolic networks, Industrial & Engineering Chemistry Research, 50, 9, 5225-5238, (2011)
[415] Qualizza, A.; Belotti, P.; Margot, F., Linear programming relaxations of quadratically constrained quadratic programs, (Lee, J.; Leyffer, S., Mixed integer nonlinear programming, The IMA Volumes in Mathematics and its Applications, 154, (2012), Springer New York), 407-426 · Zbl 1242.90155
[416] Quan, N.; Yin, J.; Ng, S. H.; Lee, L. H., Simulation optimization via Kriging: a sequential search using expected improvement with computing budget constraints, IIE Transactions, 45, 7, 763-780, (2013)
[417] Quesada, I.; Grossmann, I. E., A global optimization algorithm for linear fractional and bilinear programs, Journal of Global Optimization, 6, 1, 39-76, (1995) · Zbl 0835.90074
[418] Rashid, K.; Ambani, S.; Cetinkaya, E., An adaptive multiquadric radial basis function method for expensive black-box mixed-integer nonlinear constrained optimization, Engineering Optimization, 45, 2, 185-206, (2013)
[419] Rebennack, S.; Kallrath, J.; Pardalos, P. M., Column enumeration based decomposition techniques for a class of non-convex MINLP problems, Journal of Global Optimization, 43, 2-3, 277-297, (2009) · Zbl 1169.90417
[420] Regis, R. G., Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions, Computers & Operations Research, 38, 5, 837-853, (2011)
[421] Regis, R. G., Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points, Engineering Optimization, 46, 2, 218-243, (2014)
[422] Regis, R. G.; Shoemaker, C. A., Constrained global optimization of expensive black box functions using radial basis functions, Journal of Global Optimization, 31, 1, 153-171, (2005) · Zbl 1274.90511
[423] Regis, R. G.; Shoemaker, C. A., Improved strategies for radial basis function methods for global optimization, Journal of Global Optimization, 37, 1, 113-135, (2007) · Zbl 1149.90120
[424] Regis, R. G.; Shoemaker, C. A., Parallel radial basis function methods for the global optimization of expensive functions, European Journal of Operational Research, 182, 2, 514-535, (2007) · Zbl 1178.90279
[425] Regis, R. G.; Shoemaker, C. A., A stochastic radial basis function method for the global optimization of expensive functions, INFORMS Journal on Computing, 19, 4, 497-509, (2007) · Zbl 1241.90192
[426] Regis, R. G.; Shoemaker, C. A., Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization, Engineering Optimization, 45, 5, 529-555, (2013)
[427] Regis, R. G.; Shoemaker, C. A., A quasi-multistart framework for global optimization of expensive functions using response surface models, Journal of Global Optimization, 56, 4, 1719-1753, (2013) · Zbl 1275.90068
[428] Rendl, F.; Rinaldi, G.; Wiegele, A., Solving MAX-cut to optimality by intersecting semidefinite and polyhedral relaxations, Mathematical Programming, 121, 2, 307-335, (2010) · Zbl 1184.90118
[429] Richard, J. P.; Tawarmalani, M., Lifting inequalities: a framework for generating strong cuts for nonlinear programs, Mathematical Programming, 121, 1, 61-104, (2010) · Zbl 1184.90130
[430] Rikun, A. D., A convex envelope formula for multilinear functions, Journal of Global Optimization, 10, 425-437, (1997) · Zbl 0881.90099
[431] Rios, L. M.; Sahinidis, N. V., Portfolio optimization for wealth-dependent risk preferences, Annals of Operations Research, 177, 63-90, (2010) · Zbl 1195.91148
[432] Rios, L. M.; Sahinidis, N. V., Derivative-free optimization: a review of algorithms and comparison of software implementations, Journal of Global Optimization, 56, 3, 1247-1293, (2013) · Zbl 1272.90116
[433] Rodrigues-Fernandez, M. P.; Banga, J. R., A hybrid approach for efficient and robust parameter estimation in biochemical pathways, Biosystems, 83, 248-265, (2006)
[434] Rodrigues-Fernandez, M. P.; Egea, J.; Banga, J. R., Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems, BMC Bioinformatics, 7, 1, 483, (2006)
[435] Romero, R.; Monticelli, A.; Garcia, A.; Haffner, S., Test systems and mathematical models for transmission network expansion planning, Generation, Transmission and Distribution, IEE Proceedings-, 149, 1, 27-36, (2002)
[436] Rosen, J. B.; Pardalos, P. M., Global minimization of large-scale constrained concave quadratic problems by separable programming, Mathematical Programming, 34, 2, 163-174, (1986) · Zbl 0597.90066
[437] Ruiz, J. P. Grossmann, I. E. (2009). Water treatment network design. Available from CyberInfrastructure for MINLP [www.minlp.org, a collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=24.
[438] Ruiz, J. P.; Grossmann, I. E., Exploiting vector space properties to strengthen the relaxation of bilinear programs arising in the global optimization of process networks, Optimization Letters, 5, 1-11, (2011) · Zbl 1211.90186
[439] Ruiz, J. P.; Grossmann, I. E., Using redundancy to strengthen the relaxation for the global optimization of MINLP problems, Computers & Chemical Engineering, 35, 2729-2740, (2011)
[440] Ruiz, M.; Briant, O.; Clochard, J.-M.; Penz, B., Large-scale standard pooling problems with constrained pools and fixed demands, Journal of Global Optimization, 56, 3, 939-956, (2013) · Zbl 1275.90069
[441] Ruuth, S., Global optimization of explicit strong-stability-preserving Runge-Kutta methods, Mathematics of Computation, 75, 253, 183-207, (2006) · Zbl 1080.65088
[442] Ryoo, H. S.; Sahinidis, N. V., Global optimization of nonconvex NLPs and MINLPs with applications in process design, Computers & Chemical Engineering, 19, 5, 551-566, (1995)
[443] Ryoo, H. S.; Sahinidis, N. V., A branch-and-reduce approach to global optimization, Journal of Global Optimization, 8, 107-138, (1996) · Zbl 0856.90103
[444] Ryoo, H. S.; Sahinidis, N. V., Analysis of bounds for multilinear functions, Journal of Global Optimization, 19, 4, 403-424, (2001) · Zbl 0982.90054
[445] Sahinidis, N. V., BARON: A general purpose global optimization software package, Journal of Global Optimization, 8, 2, 201-205, (1996) · Zbl 0856.90104
[446] Saif, Y.; Elkamel, A.; Pritzker, M., Global optimization of reverse osmosis network for wastewater treatment and minimization, Industrial & Engineering Chemistry Research, 47, 9, 3060-3070, (2008)
[447] Sankaran, S.; Audet, C.; Marsden, A. L., A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation, Journal of Computational Physics, 229, 12, 4664-4682, (2010) · Zbl 1193.65100
[448] Sasena, M. J.; Papalambros, P.; Goovaerts, P., Exploration of metamodeling sampling criteria for constrained global optimization, Engineering Optimization, 34, 3, 263-278, (2002)
[449] Savola, T.; Fogelholm, C.-J., MINLP optimisation model for increased power production in small-scale CHP plants, Applied Thermal Engineering, 27, 1, 89-99, (2007)
[450] Sawaya, N. W., Reformulations, relaxations and cutting planes for generalized disjunctive programming, (2006), Carnegie Mellon University, (Ph.D. in Chemical Engineering)
[451] Saxena, A.; Bonami, P.; Lee, J., Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations, Mathematical Programming, 124, 1-2, 383-411, (2010) · Zbl 1198.90330
[452] Saxena, A.; Bonami, P.; Lee, J., Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations, Mathematical Programming, 130, 359-413, (2011) · Zbl 1229.90144
[453] Schittkowski, K., More test examples for nonlinear programming codes, Lecture Notes in Economics and Mathematical Systems, 282, (1987), Springer-Verlag · Zbl 0658.90060
[454] Scott, J.; Stuber, M.; Barton, P. I., Generalized mccormick relaxations, Journal of Global Optimization, 51, 569-606, (2011) · Zbl 1232.49033
[455] Scozzari, A.; Tardella, F., A clique algorithm for standard quadratic programming, Discrete Applied Mathematics, 156, 13, 2439-2448, (2008) · Zbl 1163.90691
[456] Selot, A.; Kuok, L. K.; Robinson, M.; Mason, T. L.; Barton, P. I., A short-term operational planning model for natural gas production systems, AIChE Journal, 54, 2, 495-515, (2008)
[457] di Serafino, D.; Gomez, S.; Milano, L.; Riccio, F.; Toraldo, G., A genetic algorithm for a global optimization problem arising in the detection of gravitational waves, Journal of Global Optimization, 48, 1, 41-55, (2010) · Zbl 1202.90221
[458] Shah, S. B.; Sahinidis, N. V., SAS-pro: simultaneous residue assignment and structure superposition for protein structure alignment, PLoS ONE, 7, 5, e37493, (2012)
[459] Sherali, H.; Dalkiran, E.; Liberti, L., Reduced RLT representations for nonconvex polynomial programming problems, Journal of Global Optimization, 52, 3, 447-469, (2012) · Zbl 1244.90185
[460] Sherali, H. D., Convex envelopes of multilinear functions over a unit hypercube and over special discrete sets, Acta Mathematica Vietnamica, 22, 1, 245-270, (1997) · Zbl 0914.90205
[461] Sherali, H. D.; Adams, W. P., A reformulation-linearization technique for solving discrete and continuous nonconvex problems, Nonconvex Optimization and Its Applications, (1999), Kluwer Academic Publishers Dordrecht, Netherlands · Zbl 0926.90078
[462] Sherali, H. D.; Alameddine, A., A new reformulation-linearization technique for bilinear programming problems, Journal of Global Optimization, 2, 379-410, (1992) · Zbl 0791.90056
[463] Sherali, H. D.; Fraticelli, B. M.P., Enhancing RLT relaxations via a new class of semidefinite cuts, Journal of Global Optimization, 22, 1-4, 233-261, (2002) · Zbl 1045.90044
[464] Sherali, H. D.; Tuncbilek, C. H., A reformulation-convexification approach for solving nonconvex quadratic-programming problems, Journal of Global Optimization, 7, 1, 1-31, (1995) · Zbl 0844.90064
[465] Sherali, H. D.; Tuncbilek, C. H., New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems, Operations Research Letters, 21, 1, 1-9, (1997) · Zbl 0885.90105
[466] Shikhman, V.; Stein, O., On jet-convex functions and their tensor products, Optimization, 61, 6, 717-731, (2012) · Zbl 1248.26017
[467] Skjäl, A.; Westerlund, T., New methods for calculating αBB-type underestimators, Journal of Global Optimization, 58, 3, 411-427, (2014) · Zbl 1305.90337
[468] Skjäl, A.; Westerlund, T.; Misener, R.; Floudas, C. A., A generalization of the classical αBB convex underestimation via diagonal and nondiagonal quadratic terms, Journal of Optimization Theory and Applications, 154, 2, 462-490, (2012) · Zbl 1256.90038
[469] Smith, E. M.B.; Pantelides, C. C., Global optimisation of nonconvex minlps, Computers & Chemical Engineering, 21, Supplement, S791-S796, (1997)
[470] Smith, E. M.B.; Pantelides, C. C., A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex minlps, Computers & Chemical Engineering, 23, 4 - 5, 457-478, (1999)
[471] Spendley, W.; Hext, G. R.; Himsworth, F. R., Sequential application of simplex designs in optimisation and evolutionary operation, Technometrics, 4, 4, 441-461, (1962) · Zbl 0121.35603
[472] Sun, J.; Garibaldi, J. M.; Krasnogor, N.; Zhang, Q., An intelligent multi-restart memetic algorithm for box constrained global optimisation, Evolutionary Computation, 21, 1, 107-147, (2013)
[473] Szabó, P. G.; Markót, C. M.; Csendes, T., Global optimization in geometry circle packing into the square, (Audet, C.; Hansen, P.; Savard, G., Essays and surveys in global optimization, (2005), Springer, New York), 233-265 · Zbl 1136.90445
[474] Tadayon, B.; Smith, J. C., Algorithms for an integer multicommodity network flow problem with node reliability considerations, Journal of Optimization Theory and Applications, 161, 506-532, (2013) · Zbl 1291.90280
[475] Tardella, F., On a class of functions attaining their maximum at the vertices of a polyhedron, Discrete Applied Mathematics, 22, 191-195, (1988/89) · Zbl 0663.90068
[476] Tardella, F., On the existence of polyhedral convex envelopes, (Floudas, C. A.; Pardalos, P. M., Frontiers in global optimization, (2003), Kluwer Academic Publishers), 563-573 · Zbl 1176.90473
[477] Tardella, F., Existence and sum decomposition of vertex polyhedral convex envelopes, Optimization Letters, 2, 363-375, (2008) · Zbl 1152.90614
[478] Tawarmalani, M.; Ahmed, S.; Sahinidis, N. V., Product disaggregation in global optimization and relaxations of rational programs, Optimization and Engineering, 3, 281-303, (2002) · Zbl 1035.90064
[479] Tawarmalani, M.; Richard, J.-P. P.; Xiong, C., Explicit convex and concave envelopes through polyhedral subdivisions, Mathematical Programming, 138, 1-2, 531-577, (2013) · Zbl 1273.90165
[480] Tawarmalani, M.; Sahinidis, N. V., Semidefinite relaxations of fractional programs via novel convexification techniques, Journal of Global Optimization, 20, 133-154, (2001) · Zbl 1001.90064
[481] Tawarmalani, M.; Sahinidis, N. V., Convex extensions and envelopes of lower semi-continuous functions, Mathematical Programming, 93, 2, 247-263, (2002) · Zbl 1065.90062
[482] Tawarmalani, M.; Sahinidis, N. V., Convexification and global optimization in continuous and mixed-integer nonlinear programming: theory, applications, software, and applications, Nonconvex Optimization and Its Applications, (2002), Kluwer Academic Publishers Norwell, MA, USA · Zbl 1031.90022
[483] Tawarmalani, M.; Sahinidis, N. V., Global optimization of mixed-integer nonlinear programs: A theoretical and computational study, Mathematical Programming, 99, 563-591, (2004) · Zbl 1062.90041
[484] Tawarmalani, M.; Sahinidis, N. V., A polyhedral branch-and-cut approach to global optimization, Mathematical Programming, 103, 225-249, (2005) · Zbl 1099.90047
[485] Teles, J.; Castro, P. M.; Novais, A. Q., LP-based solution strategies for the optimal design of industrial water networks with multiple contaminants, Chemical Engineering Science, 63, 2, 376-394, (2008)
[486] Teles, J. P.; Castro, P. M.; Matos, H. A., Global optimization of water networks design using multiparametric disaggregation, Computers & Chemical Engineering, 40, 132-147, (2012)
[487] Tsoukalas, A.; Mitsos, A., Multivariate mccormick relaxations, Journal of Global Optimization, 59, 2-3, 633-662, (2014) · Zbl 1312.90068
[488] Vandenbussche, D.; Nemhauser, G. L., A branch-and-cut algorithm for nonconvex quadratic programs with box constraints, Mathematical Programming, 102, 3, 559-575, (2005) · Zbl 1137.90010
[489] Vandenbussche, D.; Nemhauser, G. L., A polyhedral study of nonconvex quadratic programs with box constraints, Mathematical Programming, 102, 3, 531-557, (2005) · Zbl 1137.90009
[490] Vaz, A. I.F.; Vicente, L. N., A particle swarm pattern search method for bound constrained global optimization, Journal of Global Optimization, 39, 2, 197-219, (2007) · Zbl 1180.90252
[491] Vaz, A. I.F.; Vicente, L. N., Pswarm: a hybrid solver for linearly constrained global derivative-free optimization, Optimization Methods and Software, 24, 4-5, 669-685, (2009) · Zbl 1177.90327
[492] Viana, F. A.C.; Haftka, R. T.; Watson, L. T., Efficient global optimization algorithm assisted by multiple surrogate techniques, Journal of Global Optimization, 56, 2, 669-689, (2013) · Zbl 1275.90072
[493] Vicente, L. N., Implicitly and densely discrete black-box optimization problems, Optimization Letters, 3, 3, 475-482, (2009) · Zbl 1170.90441
[494] Vicente, L. N.; Custódio, A. L., Analysis of direct searches for discontinuous functions, Mathematical Programming, 133, 1-2, 299-325, (2012) · Zbl 1245.90127
[495] Vigerske, S., Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming, (2012), Humboldt-University Berlin, (Ph.D. in Mathematics
[496] Villemonteix, J.; Vazquez, E.; Sidorkiewicz, M.; Walter, E., Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria, Journal of Global Optimization, 43, 2, 373-389, (2009) · Zbl 1169.90460
[497] Villemonteix, J.; Vazquez, E.; Walter, E., An informational approach to the global optimization of expensive-to-evaluate functions, Journal of Global Optimization, 44, 4, 509-534, (2009) · Zbl 1180.90253
[498] Visweswaran, V., MINLP: applications in blending and pooling, (Floudas, C. A.; Pardalos, P. M., Encyclopedia of optimization, (2009), Springer Science), 2114-2121
[499] Visweswaran, V.; Floudas, C. A., A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: II. application of theory and test problems, Computers & Chemical Engineering, 14, 12, 1419-1434, (1990)
[500] Waki, H.; Kim, S.; Kojima, M.; Muramatsu, M., Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity, SIAM Journal on Optimization, 17, 1, 218-242, (2006) · Zbl 1109.65058
[501] Wan, X. T.; Pekny, J. F.; Reklaitis, G. V., Simulation-based optimization with surrogate models - application to supply chain management, Computers & Chemical Engineering, 29, 6, 1317-1328, (2005)
[502] Wang, B.; Gebreslassie, B. H.; You, F., Sustainable design and synthesis of hydrocarbon biorefinery via gasification pathway: integrated life cycle assessment and technoeconomic analysis with multiobjective superstructure optimization, Computers & Chemical Engineering, 52, 55-76, (2013)
[503] Wechsung, A.; Barton, P. I., Global optimization of bounded factorable functions with discontinuities, Journal of Global Optimization, 58, 1, 1-30, (2014) · Zbl 1311.90114
[504] Wechsung, A.; Schaber, S. D.; Barton, P. I., The cluster problem revisited, Journal of Global Optimization, 58, 3, 429-438, (2014) · Zbl 1297.49046
[505] Westerlund, T.; Lundell, A.; Westerlund, J., Some notes on convex relaxations, AIDIC Conference Series, 10, 383-392, (2011)
[506] Westerlund, T.; Skrifvars, H.; Harjunkoski, I.; Pörn, R., An extended cutting plane method for a class of non-convex MINLP problems, Computers & Chemical Engineering, 22, 3, 357-365, (1998)
[507] Wicaksono, D. S.; Karimi, I. A., Piecewise MILP under-and overestimators for global optimization of bilinear programs, AIChE Journal, 54, 4, 991-1008, (2008)
[508] Williams, C. M.; Ghobeity, A.; Pak, A. J.; Mitsos, A., Simultaneous optimization of size and short-term operation for an RO plant, Desalination, 301, 42-52, (2012)
[509] Wolfe, M. A., Interval mathematics, algebraic equations and optimization, Journal of Computational and Applied Mathematics, 124, 1-2, 263-280, (2000) · Zbl 0994.65052
[510] Yao, W.; Chen, X. Q.; Huang, Y. Y.; van Tooren, M., A surrogate-based optimization method with RBF neural network enhanced by linear interpolation and hybrid infill strategy, Optimization Methods and Software, 29, 2, 406-429, (2014) · Zbl 1285.90072
[511] Yee, T. F.; Grossmann, I. E., Simultaneous optimization models for heat integrationii. heat exchanger network synthesis, Computers & Chemical Engineering, 14, 10, 1165-1184, (1990)
[512] You, F.; Grossmann, I. E., Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management, Industrial & Engineering Chemistry Research, 47, 20, 7802-7817, (2008)
[513] You, F. Grossmann, I. E.(2009a). Mixed-integer nonlinear programming models and algorithms for supply chain design with stochastic inventory management. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=30.
[514] You, F. Grossmann, I. E.(2009b). Mixed-integer nonlinear programming models for the optimal design of multi-product batch plant. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=48.
[515] You, F.; Grossmann, I. E., Integrated multi-echelon supply chain design with inventories under uncertainty: MINLP models, computational strategies, AIChE Journal, 56, 2, 419-440, (2010)
[516] Yuan, Z.; Chen, B., Process synthesis for addressing the sustainable energy systems and environmental issues, AIChE Journal, 58, 11, 3370-3389, (2012)
[517] Zabinsky, Z. B., Stochastic adaptive search for global optimization, NonConvex Optimization and its Applications, (2003), Kluwer Norwel,MA
[518] Zhao, Q.; Karisch, S. E.; Rendl, F.; Wolkowicz, H., Semidefinite programming relaxations for the quadratic assignment problem, Journal of Combinatorial Optimization, 2, 71-109, (1998) · Zbl 0904.90145
[519] Zhao, Z.; Meza, J. C.; Hove, M. V., Using pattern search methods for surface structure determination of nanomaterials, Journal of Physics: Condensed Matter, 18, 39, 8693-8706, (2006)
[520] Zondervan, E. Grossmann, I. E. (2009). A deterministic security constrained unit commitment model. Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=41.
[521] Zorn, K.; Sahinidis, N. V., Computational experience with applications of bilinear cutting planes, Industrial & Engineering Chemistry Research, 52, 22, 7514-7525, (2013)
[522] Zorn, K.; Sahinidis, N. V., Global optimization of general non-convex problems with intermediate bilinear substructures, Optimization Methods and Software, 29, 3, 442-462, (2014) · Zbl 1285.90043
[523] Zorn, K.; Sahinidis, N. V., Global optimization of general nonconvex problems with intermediate polynomial substructures, Journal of Global Optimization, 59, 2-3, 673-693, (2014) · Zbl 1301.90066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.