×

zbMATH — the first resource for mathematics

ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations. (English) Zbl 1301.90063
Summary: This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks. To demonstrate the capacity of ANTIGONE, this paper presents computational results on a test suite of 2,571 problems from standard libraries and the open literature; we compare ANTIGONE to other state-of-the-art global optimization solvers.

MSC:
90C11 Mixed integer programming
90C26 Nonconvex programming, global optimization
PDF BibTeX Cite
Full Text: DOI
References:
[1] Achterberg, T, SCIP: solving constraint integer programs, Math. Program. Comput., 1, 1-41, (2009) · Zbl 1171.90476
[2] Achterberg, T., Berthold, T., Koch, T., Wolter, K.: Constraint integer programming: a new approach to integrate CP and MIP. In: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR (2008) · Zbl 1142.68504
[3] Achterberg, T; Koch, T; Martin, A, Branching rules revisited, Oper. Res. Lett., 33, 42-54, (2005) · Zbl 1076.90037
[4] Adjiman, CS; Androulakis, IP; Floudas, CA, A global optimization method, \(α \)BB, for general twice differentiable NLPs-II. implementation and computional results, Comput. Chem. Eng., 22, 1159-1179, (1998)
[5] Adjiman, CS; Dallwig, S; Floudas, CA; Neumaier, A, A global optimization method, \(α \)BB, for general twice differentiable NLPs-I. theoretical advances, Comput. Chem. Eng., 22, 1137-1158, (1998)
[6] Ahmetović, E., & Grossmann, I.E.: Integrated process water networks design problem (2010). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=101 · Zbl 0663.90068
[7] Ahmetović, E; Grossmann, IE, Global superstructure optimization for the design of integrated process water networks, AIChE J., 57, 434-457, (2011)
[8] Al-Khayyal, FA; Falk, JE, Jointly constrained biconvex programming, Math. Oper. Res., 8, 273-286, (1983) · Zbl 0521.90087
[9] Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen. D.: LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, 3rd edn (1999) · Zbl 1125.93461
[10] Androulakis, IP; Maranas, CD; Floudas, CA, \(α \)BB: A global optimization method for general constrained nonconvex problems, J. Glob. Optim., 7, 337-363, (1995) · Zbl 0846.90087
[11] Anstreicher, KM, Recent advances in the solution of quadratic assignment problems, Math. Program., 97, 27-42, (2003) · Zbl 1035.90067
[12] Anstreicher, KM, Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming, J. Glob. Optim., 43, 471-484, (2009) · Zbl 1169.90425
[13] Anstreicher, KM, On convex relaxations for quadratically constrained quadratic programming, Math. Program., 136, 233-251, (2012) · Zbl 1267.90103
[14] Audet, C; Hansen, P; Jaumard, B; Savard, G, A branch and cut algorithm for nonconvex quadratically constrained quadratic programming, Math. Program., 87, 131-152, (2000) · Zbl 0966.90057
[15] Bao, X; Sahinidis, NV; Tawarmalani, M, Multiterm polyhedral relaxations for nonconvex, quadratically-constrained quadratic programs, Optim. Methods Softw., 24, 485-504, (2009) · Zbl 1179.90252
[16] Belotti, P., Kirches, C., Leyffer, S., Linderoth, J., Luedtke, J., Mahajan, A.: Mixed-integer nonlinear optimization. Acta Numer. 22, 1-131, 5 (2013) · Zbl 1291.65172
[17] Belotti, P; Lee, J; Liberti, L; Margot, F; Wächter, A, Branching and bounds tightening techniques for non-convex MINLP, Optim. Method. Softw., 24, 597-634, (2009) · Zbl 1179.90237
[18] Berthold, T; Gleixner, AM; Heinz, S; Vigerske, S, Analyzing the computational impact of MIQCP solver components, Numer. Algebr. Control Optim., 2, 739-748, (2012) · Zbl 1269.90066
[19] Berthold, T., Heinz, S., Vigerske, S.: Extending a CIP framework to solve MIQCPs. In Lee, J., Leyffer S. (eds) Mixed Integer Nonlinear Programming, volume 154 of The IMA Volumes in Mathematics and its Applications, pp. 427-444. Springer, New York (2012) · Zbl 1242.90120
[20] Bonami, P; Biegler, LT; Conn, AR; Cornuéjols, G; Grossmann, IE; Laird, CD; Lee, J; Lodi, A; Margot, F; Sawaya, N; Wächter, A, An algorithmic framework for convex mixed integer nonlinear programs, Discret. Optim., 5, 186-204, (2008) · Zbl 1151.90028
[21] Bragalli, C; DAmbrosio, C; Lee, J; Lodi, A; Toth, P, On the optimal design of water distribution networks: a practical MINLP approach, Optim. Eng., 13, 219-246, (2012) · Zbl 1293.76045
[22] Brönnimann, H., Melquiond, G., Pion, S.: The Boost interval arithmetic library. In: Proceedings of the 5th Conference on Real Numbers and Computers, pp. 65-80. Lyon, France (2003) · Zbl 1163.90691
[23] Brönnimann, H; Melquiond, G; Pion, S, The design of the boost interval arithmetic library, Theor. Comput. Sci., 351, 111-118, (2006) · Zbl 1086.65046
[24] Burer, S; Letchford, AN, Non-convex mixed-integer nonlinear programming: a survey, Surv. Oper. Res. Manag. Sci., 17, 97-106, (2012)
[25] Burer, S; Vandenbussche, D, A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations, Math. Program., 113, 259-282, (2008) · Zbl 1135.90034
[26] Bussieck, M.R., Drud, A.S., Meeraus, A.: MINLPLib: a collection of test models for mixed-integer nonlinear programming. INFORMS J. Comput 15(1), 114-119 (2003) · Zbl 1238.90104
[27] Bussieck, MR; Vigerske, S; Cochran, JJ (ed.); Cox, LA (ed.); Keskinocak, P (ed.); Kharoufeh, JP (ed.); Smith, JC (ed.), MINLP solver software, (2010), New York
[28] Caballero, JA; Grossmann, IE, Generalized disjunctive programming model for the optimal synthesis of thermally linked distillation columns, Ind. Eng. Chem. Res., 40, 2260-2274, (2001)
[29] Caballero, JA; Grossmann, IE, Design of distillation sequences: from conventional to fully thermally coupled distillation systems, Comput. Chem. Eng., 28, 2307-2329, (2004)
[30] Caballero, JA; Grossmann, IE, Structural considerations and modeling in the synthesis of heat integrated thermally coupled distillation sequences, Ind. Eng. Chem. Res., 45, 8454-8474, (2006)
[31] Caballero, J.A., Grossmann, I.E.: Optimal separation sequences based on distillation: from conventional to fully thermally coupled systems (2009). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=69 · Zbl 0856.90103
[32] Cafieri, S; Lee, J; Liberti, L, On convex relaxations of quadrilinear terms, J. Glob. Optim., 47, 661-685, (2010) · Zbl 1202.90236
[33] Castro, P; Novais, A, Optimal periodic scheduling of multistage continuous plants with single and multiple time grid formulations, Ind. Eng. Chem. Res., 46, 3669-3683, (2007)
[34] Castro, P., Novais, A.: Periodic scheduling of continuous multiproduct plants (2009). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=34
[35] Castro, PM; Matos, HA; Novais, AQ, An efficient heuristic procedure for the optimal design of wastewater treatment systems, Resour. Conserv. Recycl., 50, 158-185, (2007)
[36] Castro, PM; Teles, JP, Comparison of global optimization algorithms for the design of water-using networks, Comput. Chem. Eng., 52, 249-261, (2013)
[37] Castro, PM; Teles, JP; Novais, AQ, Linear program-based algorithm for the optimal design of wastewater treatment systems, Clean Technol. Environ. Policy, 11, 83-93, (2009)
[38] Chang, YJ; Sahinidis, NV, Global optimization in stabilizing controller design, J. Glob. Optim., 38, 509-526, (2007) · Zbl 1125.93461
[39] Chang, Y.J., Sahinidis, N.V.: Stabilizing controller design and the belgian chocolate problem (2009). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=57 · Zbl 1292.90239
[40] D’Ambrosio, C., Bragalli, C., Lee, J., Lodi, A., Toth, P.: Optimal design of water distribution networks (2011). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=134 · Zbl 1176.90469
[41] D’Ambrosio, C; Lodi, A, Mixed integer nonlinear programming tools: an updated practical overview, Ann. Oper. Res., 204, 301-320, (2013) · Zbl 1269.90067
[42] Dolan, ED; Moré, JJ, Benchmarking optimization software with performance profiles, Math. Program., 91, 201-213, (2002) · Zbl 1049.90004
[43] Domes, F; Neumaier, A, Constraint propagation on quadratic constraints, Constraints, 15, 404-429, (2010) · Zbl 1208.68200
[44] Domes, F; Neumaier, A, Rigorous enclosures of ellipsoids and directed Cholesky factorizations, SIAM J. Matrix Anal. Appl., 32, 262-285, (2011) · Zbl 1242.90152
[45] Duran, MA; Grossmann, IE, A mixed-integer nonlinear programming algorithm for process systems synthesis, AIChE J., 32, 592-606, (1986)
[46] Duran, MA; Grossmann, IE, An outer-approximation algorithm for a class of mixed-integer nonlinear programs, Math. Program., 36, 307-339, (1986) · Zbl 0619.90052
[47] Escobar, M., Grossmann, I.E.: Mixed-integer nonlinear programming models for optimal simultaneous synthesis of heat exchangers network (2010). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=93 · Zbl 0619.90052
[48] Flores-Tlacuahuac, A., Grossmann, I.E.: Simultaneous cyclic scheduling and control of a multiproduct cstr (2009). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=71 · Zbl 1257.90079
[49] Floudas, C.A.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, New York (1995) · Zbl 0886.90106
[50] Floudas, C.A.: Deterministic Global Optimization : Theory, Methods and Applications. Nonconvex Optimization and Its Applications. Kluwer, Dordrecht (2000)
[51] Floudas, CA; Akrotirianakis, IG; Caratzoulas, S; Meyer, CA; Kallrath, J, Global optimization in the 21st century: advances and challenges, Comput. Chem. Eng., 29, 1185-1202, (2005)
[52] Floudas, CA; Gounaris, CE, A review of recent advances in global optimization, J. Glob. Optim., 45, 3-38, (2009) · Zbl 1180.90245
[53] Floudas, CA; Pardalos, PM, State-of-the-art in global optimization: computational methods and applications—preface, J. Glob. Optim., 7, 113, (1995)
[54] Floudas, C.A., Pardalos, P.M., Adjiman, C.S., Esposito, W.R., Gümüs, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., Schweiger, C.A.: Handbook of Test Problems in Local and Global Optimization. Kluwer, Dordrecht (1999) · Zbl 0943.90001
[55] Fourer, R., Gay, D.M., Kernighan, B.W.: The AMPL Book. AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, Brooks/Cole Publishing Company, Stamford (2002) · Zbl 0701.90062
[56] Fourer, R; Maheshwari, C; Neumaier, A; Orban, D; Schichl, H, Convexity and concavity detection in computational graphs: tree walks for convexity assessment, INFORMS J. Comput, 22, 26-43, (2010) · Zbl 1243.90004
[57] Gatzke, EP; Tolsma, JE; Barton, PI, Construction of convex relaxations using automated code generation techniques, Optim. Eng., 3, 305-326, (2002) · Zbl 1035.90063
[58] Gau, CY; Schrage, LE; Floudas, CA (ed.); Pardalos, PM (ed.), Implementation and testing of a branch-and-bound based method for deterministic global optimization: operations research applications, 145-164, (2003), Dordrecht
[59] Geoffrion, AM, Elements of large-scale mathematical programming. 1. concepts, Manag. Sci. Ser. Theory, 16, 652-675, (1970) · Zbl 0209.22801
[60] Gopalakrishnan, A., Biegler, L.: MINLP and MPCC formulations for the cascading tanks problem (2011). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=140 · Zbl 1242.90137
[61] Gounaris, C.E., First, E.L., Floudas, C.A.: Estimation of diffusion anisotropy in microporous crystalline materials and optimization of crystal orientation in membranes. J. Chem. Phys. 139(12), 124703 (2013)
[62] Gounaris, CE; Floudas, CA, Convexity of products of univariate functions and convexification transformations for geometric programming, J. Optim. Theory Appl., 138, 407-427, (2008) · Zbl 1163.90017
[63] Grossmann, IE, Advances in mathematical programming models for enterprise-wide optimization, Comput. Chem. Eng., 47, 2-18, (2012)
[64] Grossmann, IE; Guillén-Gosálbez, G, Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes, Comput. Chem. Eng., 34, 1365-1376, (2010)
[65] Grossmann, IE; Sargent, RWH, Optimum design of multipurpose chemical plants, Ind. Eng. Chem. Process Des. Dev., 18, 343-348, (1979)
[66] Guillén-Gosálbez, G., Pozo, C.: Optimization of metabolic networks in biotechnology (2010). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=81
[67] 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 Bioinform. 10, 386 (2009) · Zbl 1282.90141
[68] Kallrath, J, Cutting circles and polygons from area-minimizing rectangles, J. Glob. Optim., 43, 299-328, (2009) · Zbl 1169.90434
[69] Kallrath, J., Rebennack, S.: Cutting ellipses from area-minimizing rectangles. J. Glob. Optim. 1-33 (2013). doi:10.1007/s10898-013-0125-3 · Zbl 1301.90073
[70] Karuppiah, R; Grossmann, IE, Global optimization for the synthesis of integrated water systems in chemical processes, Comput. Chem. Eng., 30, 650-673, (2006)
[71] Khajavirad, A; Sahinidis, NV, Convex envelopes of products of convex and component-wise concave functions, J. Glob. Optim., 52, 391-409, (2012) · Zbl 1268.90052
[72] Khajavirad, A; Sahinidis, NV, Convex envelopes generated from finitely many compact convex sets, Math. Program., 137, 371-408, (2013) · Zbl 1284.90055
[73] Khor, C.S., Chachuat, B., Shah, N.: Fixed-flowrate total water network synthesis under uncertainty with risk management. J. Clean. Prod. (2014). doi:10.1016/j.jclepro.2014.01.023
[74] Kocis, GR; Grossmann, IE, Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis, Ind. Eng. Chem. Res., 27, 1407-1421, (1988)
[75] Kolodziej, SP; Castro, PM; Grossmann, IE, Global optimization of bilinear programs with a multiparametric disaggregation technique, J. Glob. Optim., 57, 1039-1063, (2013) · Zbl 1282.90137
[76] Kolodziej, SP; Grossmann, IE; Furman, KC; Sawaya, NW, A discretization-based approach for the optimization of the multiperiod blend scheduling problem, Comput. Chem. Eng., 53, 122-142, (2013)
[77] Lebbah, Y; Michel, C; Rueher, M, A rigorous global filtering algorithm for quadratic constraints, Constraints, 10, 47-65, (2005) · Zbl 1066.90090
[78] Lee, H; Pinto, JM; Grossmann, IE; Park, S, Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management, Ind. Eng. Chem. Res., 35, 1630-1641, (1996)
[79] Li, J; Li, A; Karimi, IA; Srinivasan, R, Improving the robustness and efficiency of crude scheduling algorithms, AIChE J., 53, 2659-2680, (2007)
[80] Li, J; Misener, R; Floudas, CA, Continuous-time modeling and global optimization approach for scheduling of crude oil operations, AIChE J., 58, 205-226, (2012)
[81] Li, X; Armagan, E; Tomasgard, A; Barton, PI, Stochastic pooling problem for natural gas production network design and operation under uncertainty, AIChE J., 57, 2120-2135, (2011)
[82] Li, X; Tomasgard, A; Barton, PI, Decomposition strategy for the stochastic pooling problem, J. Glob. Optim., 54, 765-790, (2012) · Zbl 1282.90141
[83] Liberti, L; Pantelides, CC, Convex envelopes of monomials of odd degree, J. Glob. Optim., 25, 157-168, (2003) · Zbl 1030.90117
[84] Liberti, L; Pantelides, CC, An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms, J. Glob. Optim., 36, 161-189, (2006) · Zbl 1131.90045
[85] Lin, Y; Schrage, L, The global solver in the LINDO API, Optim. Methods Softw., 24, 657-668, (2009) · Zbl 1177.90325
[86] Locatelli, M., Schoen, F.: On convex envelopes for bivariate functions over polytopes. Math. Program. (2012). doi:10.1007/s10107-012-0616-x · Zbl 1295.90055
[87] Loiola, EM; Maia de Abreu, NM; Boaventura-Netto, PO; Hahn, P; Querido, T, A survey for the quadratic assignment problem, Eur. J. Oper. Res., 176, 657-690, (2007) · Zbl 1103.90058
[88] Lougee-Heimer, R, The common optimization interface for operations research: promoting open-source software in the operations research community, IBM J. Res. Dev., 47, 57-66, (2003)
[89] Lundell, A; Skjäl, A; Westerlund, T, A reformulation framework for global optimization, J. Glob. Optim., 57, 115-141, (2013) · Zbl 1277.90102
[90] Lundell, A; Westerlund, J; Westerlund, T, Some transformation techniques with applications in global optimization, J. Glob. Optim., 43, 391-405, (2009) · Zbl 1169.90453
[91] Lundell, A; Westerlund, T, Convex underestimation strategies for signomial functions, Optim. Methods Softw., 24, 505-522, (2009) · Zbl 1178.90278
[92] Lundell, A; Westerlund, T; Lee, J (ed.); Leyffer, S (ed.), Global optimization of mixed-integer signomial programming problems, 349-369, (2012), New York · Zbl 1242.90137
[93] Maranas, CD; Floudas, CA, Finding all solutions of nonlinearly constrained systems of equations, J. Glob. Optim., 7, 143-182, (1995) · Zbl 0841.90115
[94] Maranas, CD; Floudas, CA, Global optimization in generalized geometric programming, Comput. Chem. Eng., 21, 351-369, (1997)
[95] McCormick, GP, Computability of global solutions to factorable nonconvex programs: part 1-convex underestimating problems, Math. Program., 10, 147-175, (1976) · Zbl 0349.90100
[96] McDonald, CM; Floudas, CA, Glopeq: a new computational tool for the phase and chemical equilibrium problem, Comput. Chem. Eng., 21, 1-23, (1996)
[97] Meeraus, A.: GLOBALLib. http://www.gamsworld.org/global/globallib.htm
[98] Meyer, CA; Floudas, CA; Floudas, CA (ed.); Pardalos, PM (ed.), Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes, 327-352, (2003), Dordrecht · Zbl 1176.90469
[99] Meyer, CA; Floudas, CA, Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes, J. Glob. Optim., 29, 125-155, (2004) · Zbl 1085.90047
[100] Meyer, CA; Floudas, CA, Convex envelopes for edge-concave functions, Math. Program., 103, 207-224, (2005) · Zbl 1099.90045
[101] Misener, R; Floudas, CA, Advances for the pooling problem: modeling, global optimization, and computational studies, Appl. Comput. Math., 8, 3-22, (2009) · Zbl 1188.90287
[102] Misener, R; Floudas, CA, Global optimization of mixed-integer models with quadratic and signomial functions: a review, Appl. Comput. Math., 11, 317-336, (2012) · Zbl 1292.90239
[103] Misener, R; Floudas, CA, Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations, Math. Program. B, 136, 155-182, (2012) · Zbl 1257.90079
[104] Misener, R., Floudas, C.A.: A framework for globally optimizing mixed-integer signomial programs. J. Optim. Theory Appl. (2013). doi:10.1007/s10957-013-0396-3 · Zbl 1303.90074
[105] Misener, R; Floudas, CA, Glomiqo: global mixed-integer quadratic optimizer, J. Glob. Optim., 57, 3-50, (2013) · Zbl 1272.90034
[106] 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. 2012. Submitted for Publication · Zbl 1325.90071
[107] Misener, R; Thompson, JP; Floudas, CA, APOGEE: global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes, Comput. Chem. Eng., 35, 876-892, (2011)
[108] Mitsos, A; Chachuat, B; Barton, PI, Mccormick-based relaxations of algorithms, SIAM J. Optim., 20, 573-601, (2009) · Zbl 1192.65083
[109] Mouret, S., Grossmann, I.E.: Crude-oil operations scheduling (2010). Available from CyberInfrastructure for MINLP [A collaboration of Carnegie Mellon University and IBM Research] at: www.minlp.org/library/problem/index.php?i=117
[110] Mouret, S; Grossmann, IE; Pestiaux, P, A novel priority-slot based continuous-time formulation for crude-oil scheduling problems, Ind. Eng. Chem. Res., 48, 8515-8528, (2009)
[111] Neun, W., Sturm, T., Vigerske, S. (2010) Supporting global numerical optimization of rational functions by generic symbolic convexity tests. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing, volume 6244 of Lecture Notes in Computer Science, pp. 205-219 (2010) · Zbl 1290.65053
[112] Niknam, T; Khodaei, A; Fallahi, F, A new decomposition approach for the thermal unit commitment problem, Appl. Energy, 86, 1667-1674, (2009)
[113] Nowak, I.: Relaxation and decomposition methods for mixed integer nonlinear programming. International series of numerical mathematics, Birkhäuser (2005). ISBN 9783764372385
[114] Nyberg, A., Grossmann, I.E., Westerlund, T.: The optimal design of a three-echelon supply chain with inventories under uncertainty (2012). 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 · Zbl 1202.90236
[115] Nyberg, A; Grossmann, IE; Westerlund, T, An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands, AIChE J., 59, 23-28, (2013)
[116] Quesada, I; Grossmann, IE, A global optimization algorithm for linear fractional and bilinear programs, J. Glob. Optim., 6, 39-76, (1995) · Zbl 0835.90074
[117] Ruiz, J.P., Grossmann, I.E.: Water treatment network design (2009). 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 · Zbl 1179.90252
[118] Ryoo, HS; Sahinidis, NV, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Comput. Chem. Eng., 19, 551-566, (1995)
[119] Ryoo, HS; Sahinidis, NV, A branch-and-reduce approach to global optimization, J. Glob. Optim., 8, 107-138, (1996) · Zbl 0856.90103
[120] Sawaya, N.W.: Reformulations, relaxations and cutting planes for generalized disjunctive programming. Carnegie Mellon University, PhD in Chemical Engineering (2006) · Zbl 1035.90067
[121] Saxena, A; Bonami, P; Lee, J, Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations, Math. Program., 124, 383-411, (2010) · Zbl 1198.90330
[122] Scozzari, A; Tardella, F, A clique algorithm for standard quadratic programming, Discret. Appl. Math., 156, 2439-2448, (2008) · Zbl 1163.90691
[123] Selot, A; Kuok, LK; Robinson, M; Mason, TL; Barton, PI, A short-term operational planning model for natural gas production systems, AIChE J., 54, 495-515, (2008)
[124] Sherali, H; Dalkiran, E; Liberti, L, Reduced RLT representations for nonconvex polynomial programming problems, J. Glob. Optim., 52, 447-469, (2012) · Zbl 1244.90185
[125] Sherali, H.D., Adams, W.P.: A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Nonconvex Optimization and Its Applications. Kluwer, Dordrecht (1999) · Zbl 0926.90078
[126] Sherali, HD; Alameddine, A, A new reformulation-linearization technique for bilinear programming problems, J. Glob. Optim., 2, 379-410, (1992) · Zbl 0791.90056
[127] Sherali, H.D., Tuncbilek, C.H.: A reformulation-convexification approach for solving nonconvex quadratic-programming problems. J. Glob. Optim. (7): 1, 1-31 (1995) · Zbl 0844.90064
[128] Sherali, HD; Tuncbilek, CH, New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems, Oper. Res. Lett., 21, 1-9, (1997) · Zbl 0885.90105
[129] Shikhman, V; Stein, O, On jet-convex functions and their tensor products, Optimization, 61, 717-731, (2012) · Zbl 1248.26017
[130] Smith, EMB; Pantelides, CC, A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex minlps, Comput. Chem. Eng., 23, 457-478, (1999)
[131] Tadayon, B., Smith, J.C.: Algorithms for an integer multicommodity network flow problem with node reliability considerations. J. Optim. Theory Appl. (2013). doi:10.1007/s10957-013-0378-5. · Zbl 1291.90280
[132] Tardella, F, On a class of functions attaining their maximum at the vertices of a polyhedron, Discret. Appl. Math., 22, 191-195, (1988/89) · Zbl 0663.90068
[133] Tardella, F; Floudas, CA (ed.); Pardalos, PM (ed.), On the existence of polyhedral convex envelopes, 563-573, (2003), Dordrecht · Zbl 1176.90473
[134] Tardella, F, Existence and sum decomposition of vertex polyhedral convex envelopes, Optim. Lett., 2, 363-375, (2008) · Zbl 1152.90614
[135] Tawarmalani, M; Richard, J-PP; Xiong, C, Explicit convex and concave envelopes through polyhedral subdivisions, Math. Program., 138, 531-577, (2013) · Zbl 1273.90165
[136] Tawarmalani, M; Sahinidis, NV, Semidefinite relaxations of fractional programs via novel convexification techniques, J. Glob. Optim., 20, 133-154, (2001) · Zbl 1001.90064
[137] 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. Kluwer, Norwell (2002) · Zbl 1031.90022
[138] Tawarmalani, M; Sahinidis, NV, Global optimization of mixed-integer nonlinear programs: a theoretical and computational study, Math. Program., 99, 563-591, (2004) · Zbl 1062.90041
[139] Tawarmalani, M; Sahinidis, NV, A polyhedral branch-and-cut approach to global optimization, Math. Program., 103, 225-249, (2005) · Zbl 1099.90047
[140] Teles, J; Castro, PM; Novais, AQ, Lp-based solution strategies for the optimal design of industrial water networks with multiple contaminants, Chem. Eng. Sci., 63, 376-394, (2008)
[141] Teles, JP; Castro, PM; Matos, HA, Global optimization of water networks design using multiparametric disaggregation, Comput. Chem. Eng., 40, 132-147, (2012)
[142] Vandenbussche, D; Nemhauser, GL, A branch-and-cut algorithm for nonconvex quadratic programs with box constraints, Math. Program., 102, 559-575, (2005) · Zbl 1137.90010
[143] Vandenbussche, D; Nemhauser, GL, A polyhedral study of nonconvex quadratic programs with box constraints, Math. Program., 102, 531-557, (2005) · Zbl 1137.90009
[144] Vigerske, S.: COIN-OR/GAMSLinks. https://projects.coin-or.org/GAMSlinks/ (2011)
[145] Vigerske, S.: Decomposition in Multistage Stochastic Programming and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming. Humboldt-University Berlin, PhD in Mathematics (2012)
[146] Yee, TF; Grossmann, IE, Simultaneous optimization models for heat integrationii. heat exchanger network synthesis, Comput. Chem. Eng., 14, 1165-1184, (1990)
[147] You, F; Grossmann, IE, Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management, Ind. Eng. Chem. Res., 47, 7802-7817, (2008)
[148] You, F., Grossmann, I.E.: Mixed-integer nonlinear programming models and algorithms for supply chain design with stochastic inventory management (2009a). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=3
[149] You, F., Grossmann, I.E.: Mixed-integer nonlinear programming models for the optimal design of multi-product batch plant (2009b). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=48 · Zbl 1086.65046
[150] You, F; Grossmann, IE, Integrated multi-echelon supply chain design with inventories under uncertainty: MINLP models, computational strategies, AIChE J., 56, 419-440, (2010)
[151] Zondervan, E., Grossmann, I.E.: A deterministic security constrained unit commitment model (2009). Available from CyberInfrastructure for MINLP [A collaboration of CMU and IBM Research] at: www.minlp.org/library/problem/index.php?i=41
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.