zbMATH — the first resource for mathematics

QPLIB: a library of quadratic programming instances. (English) Zbl 1435.90099
Summary: This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the variety of QP solution methods, ranging from entirely combinatorial approaches to completely continuous algorithms, including many methods for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the different, interested communities is therefore important. We propose a simple taxonomy for QP instances leading to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.

90C20 Quadratic programming
90C11 Mixed integer programming
Full Text: DOI
[1] Achterberg, T.: SCIP: solving constraint integer programs. Math. Prog. Comput. 1(1), 1-41 (2009) · Zbl 1171.90476
[2] Adachi, S., Iwata, S., Nakatsukasa, Y., Takeda, A.: Solving the trust-region subproblem by a generalized eigenvalue problem. SIAM J. Optim. 27(1), 269-291 (2017) · Zbl 1359.49009
[3] Ahmetović, E., Grossmann, I.E.: Global superstructure optimization for the design of integrated process water networks. AIChE J. 57(2), 434-457 (2011)
[4] Alfaki, M., Haugland, D.: A multi-commodity flow formulation for the generalized pooling problem. J. Global Optim. 56(3), 917-937 (2013) · Zbl 1272.90103
[5] Andersen, E., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Prog. 95(2), 249-277 (2003) · Zbl 1030.90137
[6] Andersen, ED; Andersen, KD; Frenk, H. (ed.); Roos, K. (ed.); Terlaky, T. (ed.); Zhang, S. (ed.), The Mosek interior point optimizer for linear programming: an implementation of the homogeneous algorithm, 197-232 (2000), Boston · Zbl 1028.90022
[7] Anjos, MF; Liers, F.; Anjos, MF (ed.); Lasserre, JB (ed.), Global approaches for facility layout and VLSI floorplanning, No. 166, 849-877 (2012), Boston · Zbl 1334.90096
[8] Anstreicher, K.M.: Recent advances in the solution of quadratic assignment problems. Math. Prog. 97(1-2), 27-42 (2003) · Zbl 1035.90067
[9] Audet, C., Guillou, A., Hansen, P., Messine, F., Perron, S.: The small hexagon and heptagon with maximum sum of distances between vertices. J. Global Optim. 49(3), 467-480 (2011) · Zbl 1211.90258
[10] Audet, C., Hansen, P., Messine, F.: The small octagon with longest perimeter. J. Comb. Theory Ser. A 114(1), 135-150 (2007) · Zbl 1259.90096
[11] Audet, C., Hansen, P., Messine, F.: Simple polygons of maximum perimeter contained in a unit disk. Discrete Comput. Geom. 41(2), 208-215 (2009) · Zbl 1166.52003
[12] Audet, C., Hansen, P., Messine, F., Xiong, J.: The largest small octagon. J. Comb. Theory Ser. A 98(1), 46-59 (2002) · Zbl 1022.90013
[13] Audet, C., Ninin, J.: Maximal perimeter, diameter and area of equilateral unit-width convex polygons. J. Global Optim. 56(3), 1007-1016 (2013) · Zbl 1272.90055
[14] Bagajewicz, M.: A review of recent design procedures for water networks in refineries and process plants. Comput. Chem. Eng. 24(9-10), 2093-2113 (2000)
[15] Belotti, P., Lee, J., Liberti, L., Margot, F., Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24(4-5), 597-634 (2009) · Zbl 1179.90237
[16] Best, M.J.: Quadratic Programming with Computer Programs. Advances in Applied Mathematics, vol. 1. Chapman and Hall, London (2017) · Zbl 1368.90001
[17] Billionnet, A., Elloumi, S., Lambert, A.: An efficient compact quadratic convex reformulation for general integer quadratic programs. Comput. Optim. Appl. 54(1), 141-162 (2013) · Zbl 1267.90092
[18] Billionnet, A., Elloumi, S., Plateau, M.: Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: the QCR method. Discrete Appl. Math. 157(6), 1185-1197 (2009) · Zbl 1169.90405
[19] Bixby, ER; Fenelon, M.; Gu, Z.; Rothberg, E.; Wunderling, R.; Powell, MJD (ed.); Scholtes, S. (ed.), MIP: theory and practice – closing the gap, 19-49 (2000), Boston · Zbl 0986.90025
[20] Bley, A.; Gleixner, AM; Koch, T.; Vigerske, S.; Bock, HG (ed.); Hoang, XP (ed.); Rannacher, R. (ed.); Schlöder, JP (ed.), Comparing MIQCP solvers to a specialised algorithm for mine production scheduling, 25-39 (2012), Berlin
[21] Blum, L., Shub, M., Smale, S.: On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions, and universal machines. Bull. Am. Math. Soc. 21(1), 1-46 (1989) · Zbl 0681.03020
[22] Bomze, IM; Budinich, M.; Pardalos, PM; Pelillo, M.; Du, DZ (ed.); Pardalos, PM (ed.), The maximum clique problem, 1-74 (1999), Boston · Zbl 1253.90188
[23] Bonami, P., Biegler, L.T., Conn, A.R., Cornuéjols, G., Grossmann, I.E., Laird, C.D., Lee, J., Lodi, A., Margot, F., Sawaya, N., Wächter, A.: An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optim. 5(2), 186-204 (2008) · Zbl 1151.90028
[24] Bragalli, C., D’Ambrosio, C., Lee, J., Lodi, A., Toth, P.: On the optimal design of water distribution networks: a practical MINLP approach. Optim. Eng. 13(2), 219-246 (2012) · Zbl 1293.76045
[25] Buchheim, C., Wiegele, A.: Semidefinite relaxations for non-convex quadratic mixed-integer programming. Math. Program. 141(1), 435-452 (2013) · Zbl 1280.90091
[26] Burer, S.; Anjos, FM (ed.); Lasserre, BJ (ed.), Copositive programming, 201-218 (2012), Boston
[27] Burer, S.; Saxena, A.; Lee, J. (ed.); Leyffer, S. (ed.), The MILP road to MIQCP, No. 154, 373-405 (2012), Boston · Zbl 1242.90122
[28] Bussieck, MR; Vigerske, S.; C, JJ (ed.); etal., MINLP solver software (2010), London
[29] Byrd, RH; Nocedal, J.; Waltz, R.; Pillo, G. (ed.); Roma, M. (ed.), KNITRO: an integrated package for nonlinear optimization (2006), Boston · Zbl 1108.90004
[30] 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. Comput. Chem. Eng. 30(1), 54-69 (2005)
[31] Castillo, P.A.C., Mahalec, V., Kelly, J.D.: Inventory pinch algorithm for gasoline blend planning. AIChE J. 59(10), 3748-3766 (2013)
[32] Castro, J., Frangioni, A., Gentile, C.: Perspective reformulations of the CTA Problem with \[L_2\] L2 distances. Oper. Res. 62(4), 891-909 (2014) · Zbl 1302.90138
[33] Castro, P.M., Teles, J.P.: Comparison of global optimization algorithms for the design of water-using networks. Comput. Chem. Eng. 52, 249-261 (2013)
[34] Conn, A.R., Gould, N.I.M., Orban, D., Toint, P.L.: A primal-dual trust-region algorithm for non-convex nonlinear programming. Math. Program. 87(2), 215-249 (2000) · Zbl 0970.90116
[35] Dakin, R.: A tree search algorithm for mixed programming problems. Comput. J. 8(3), 250-255 (1965) · Zbl 0154.42004
[36] D’Ambrosio, C.; Linderoth, J.; Luedtke, J.; Günlük, O. (ed.); Woeginger, GJ (ed.), Valid inequalities for the pooling problem with binary variables, No. 6655, 117-129 (2011), Berlin · Zbl 1339.90238
[37] 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. J. Syst. Sci. Syst. Eng. 22(4), 385-400 (2013)
[38] Dong, H.: Relaxing nonconvex quadratic functions by multiple adaptive diagonal perturbations. SIAM J. Optim. 26(3), 1962-1985 (2016) · Zbl 1348.90473
[39] Dorneich, M.C., Sahinidis, N.V.: Global optimization algorithms for chip layout and compaction. Eng. Optim. 25(2), 131-154 (1995)
[40] Dostál, Z.: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities. Springer, Heidelberg (2009) · Zbl 1401.90013
[41] Drud, A.: CONOPT: a GRG code for large sparse dynamic nonlinear optimization problems. Math. Program. 31(2), 153-191 (1985) · Zbl 0557.90088
[42] Drud, A.S.: CONOPT: a large-scale GRG code. INFORMS J. Comput. 6(2), 207-216 (1994) · Zbl 0806.90113
[43] Drud, A.S.: SBB. ARKI Consulting and Development A/S (2017). https://www.gams.com/25.0/docs/S_SBB.html. Accessed Sept 2017
[44] Dür, M.; Diehl, M. (ed.); Glineur, F. (ed.); Jarlebring, E. (ed.); Michiels, W. (ed.), Copositive programming: a survey, 3-20 (2010), Berlin
[45] Duran, M.A., Grossmann, I.E.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36(3), 307-339 (1986) · Zbl 0619.90052
[46] Erway, J.B., Gill, P.E.: A subspace minimization method for the trust-region step. SIAM J. Optim. 20(3), 1439-1461 (2010) · Zbl 1195.49042
[47] 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 J. 58(8), 2320-2335 (2012)
[48] FICO: Xpress optimization suite (2017). http://www.fico.com/en/products/fico-xpress-optimization-suite. Accessed Sept 2017
[49] Fletcher, R.: Stable reduced Hessian updates for indefinite quadratic programming. Math. Program. 87(2), 251-264 (2000) · Zbl 0964.65065
[50] Floudas, C., Visweswaran, V.: A global optimization algorithm (GOP) for certain classes of nonconvex NLPs-I. Theory Comput. Chem. Eng. 14(12), 1397-1417 (1990)
[51] Frangioni, A., Furini, F., Gentile, C.: Approximated perspective relaxations: a project and lift approach. Comput. Optim. Appl. 63(3), 705-735 (2016) · Zbl 1362.90301
[52] Frangioni, A., Galli, L., Scutellà, M.: Delay-constrained shortest paths: approximation algorithms and second-order cone models. J. Optim. Theory Appl. 164(3), 1051-1077 (2015) · Zbl 1321.90086
[53] Frangioni, A., Galli, L., Stea, G.: Delay-constrained routing problems: accurate scheduling models and admission control. Comput. Oper. Res. 81, 67-77 (2017) · Zbl 1391.90264
[54] Frangioni, A., Gentile, C.: Perspective cuts for a class of convex 0-1 mixed integer programs. Math. Program. 106(2), 225-236 (2006) · Zbl 1134.90447
[55] Frangioni, A., Gentile, C.: SDP diagonalizations and perspective cuts for a class of nonseparable MIQP. Oper. Res. Lett. 35(2), 181-185 (2007) · Zbl 1149.90379
[56] Frangioni, A., Gentile, C.: A computational comparison of reformulations of the perspective relaxation: SOCP vs cutting planes. Oper. Res. Lett. 37(3), 206-210 (2009) · Zbl 1167.90604
[57] Frangioni, A., Gentile, C., Grande, E., Pacifici, A.: Projected perspective reformulations with applications in design problems. Oper. Res. 59(5), 1225-1232 (2011) · Zbl 1235.90148
[58] Geissler, B.; Morsi, A.; Schewe, L.; Jünger, M. (ed.); Reinelt, G. (ed.), A new algorithm for MINLP applied to gas transport energy cost minimization, 321-353 (2013), Berlin · Zbl 1317.90209
[59] Gentilini, I., Margot, F., Shimada, K.: The travelling salesman problem with neighbourhoods: MINLP solution. Optim. Methods Softw. 28(2), 364-378 (2013) · Zbl 1270.90055
[60] Gertz, E.M., Wright, S.J.: Object-oriented software for quadratic programming. ACM Trans. Math. Softw. 29(1), 58-81 (2003) · Zbl 1068.90586
[61] Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4), 979-1006 (2002) · Zbl 1027.90111
[62] Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47(1), 99-131 (2005) · Zbl 1210.90176
[63] Gill, P.E., Wong, E.: Methods for convex and general quadratic programming. Math. Program. Comput. 7(1), 71-112 (2015) · Zbl 1317.90225
[64] Gleixner, A.M., Held, H., Huang, W., Vigerske, S.: Towards globally optimal operation of water supply networks. Numer. Algebra Control Optim. 2(4), 695-711 (2012) · Zbl 1269.90083
[65] Gould, N.I.M., Lucidi, S., Roma, M., Toint, P.L.: Solving the trust-region subproblem using the Lanczos method. SIAM J. Optim. 9(2), 504-525 (1999) · Zbl 1047.90510
[66] Gould, N.I.M., Orban, D., Robinson, D.P.: Trajectory-following methods for large-scale degenerate convex quadratic programming. Math. Program. Comput. 5(2), 113-142 (2013) · Zbl 1272.65051
[67] Gould, N.I.M., Orban, D., Toint, P.L.: GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29(4), 353-372 (2003) · Zbl 1068.90525
[68] Gould, N.I.M., Robinson, D.P.: A dual gradient-projection method for large-scale strictly convex quadratic problems. Comput. Optim. Appl. 67(1), 1-38 (2017) · Zbl 1401.90142
[69] Gould, N.I.M., Robinson, D.P., Thorne, H.S.: On solving trust-region and other regularised subproblems in optimization. Math. Program. Comput. 2(1), 21-57 (2010) · Zbl 1193.65098
[70] Gould, N.I.M., Toint, PhL: A Quadratic Programming Bibliography. Numerical Analysis Group Internal Report 2000-1. Rutherford Appleton Laboratory, Chilton (2000)
[71] Gould, N.I.M., Toint, P.L.: An iterative working-set method for large-scale non-convex quadratic programming. Appl. Numer. Math. 43(1-2), 109-128 (2002) · Zbl 1012.65054
[72] 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), 124,703 (2013)
[73] Hager, W.W.: Minimizing a quadratic over a sphere. SIAM J. Optim. 12(1), 188-208 (2001) · Zbl 1058.90045
[74] Hasan, M.M.F., Karimi, I.A., Avison, C.M.: Preliminary synthesis of fuel gas networks to conserve energy and preserve the environment. Ind. Eng. Chem. Res. 50(12), 7414-7427 (2011)
[75] Hemmecke, R.; Köppe, M.; Lee, J.; Weismantel, R.; Jünger, M. (ed.); Liebling, MT (ed.); Naddef, D. (ed.); Nemhauser, LG (ed.); Pulleyblank, RW (ed.); Reinelt, G. (ed.); Rinaldi, G. (ed.); Wolsey, AL (ed.), Nonlinear integer programming, 561-618 (2010), Berlin
[76] Hifi, M., M’Hallah, R.: A literature review on circle and sphere packing problems: models and methodologies. Adv. Oper. Res. 2009, 22 (2009) · Zbl 1198.90337
[77] IBM ILOG: CPLEX Optimization Studio, 12.7.0 edn. (2016). http://www.ibm.com/support/knowledgecenter/SSSA5P
[78] Jeroslow, R.: There cannot be any algorithm for integer programming with quadratic constraints. Oper. Res. 21(1), 221-224 (1973) · Zbl 0257.90029
[79] Jeżowski, J.: Review of water network design methods with literature annotations. Ind. Eng. Chem. Res. 49(10), 4475-4516 (2010)
[80] Kallrath, J.; Floudas, CA (ed.); Pardalos, PM (ed.), Exact computation of global minima of a nonconvex portfolio optimization problem, 237-254 (2003), Alphen aan den Rijn
[81] Kallrath, J.: Cutting circles and polygons from area-minimizing rectangles. J. Global Optim. 43(2-3), 299-328 (2009) · Zbl 1169.90434
[82] Kallrath, J., Rebennack, S.: Cutting ellipses from area-minimizing rectangles. J. Global Optim. 59(2-3), 405-437 (2014) · Zbl 1301.90073
[83] Khor, C.S., Chachuat, B., Shah, N.: Fixed-flowrate total water network synthesis under uncertainty with risk management. J. Clean. Prod. 77, 79-93 (2014)
[84] Koch, T., Achterberg, T., Andersen, E., Bastert, O., Berthold, T., Bixby, R.E., Danna, E., Gamrath, G., Gleixner, A.M., Heinz, S., Lodi, A., Mittelmann, H., Ralphs, T., Salvagnin, D., Steffy, D.E., Wolter, K.: MIPLIB 2010. Math. Program. Comput. 3(2), 103-163 (2011)
[85] Kochenberger, G., Hao, J.K., Glover, F., Lewis, M., Lü, Z., Wang, H., Wang, Y.: The unconstrained binary quadratic programming problem: a survey. J. Comb. Optim. 28(1), 58-81 (2014) · Zbl 1303.90066
[86] Kocis, G.R., Grossmann, I.E.: Computational experience with DICOPT solving MINLP problems in process systems engineering. Comput. Chem. Eng. 13(3), 307-315 (1989)
[87] Kolodziej, S.P., Castro, P.M., Grossmann, I.E.: Global optimization of bilinear programs with a multiparametric disaggregation technique. J. Global Optim. 57(4), 1039-1063 (2013) · Zbl 1282.90137
[88] 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. Comput. Chem. Eng. 53, 122-142 (2013)
[89] Krislock, N., Malick, J., Roupin, F.: BiqCrunch: a semidefinite branch-and-bound method for solving binary quadratic problem. ACM Trans. Math. Softw. 43(4), 32:1-32:23 (2017) · Zbl 1380.90284
[90] Land, A., Doig, A.: An automatic method of solving discrete programming problems. Econometrica 28(3), 497-520 (1960) · Zbl 0101.37004
[91] Lasdon, L., Plummer, J., Ugray, Z., Bussieck, M.: Improved Filters and Randomized Drivers for Multi-start Global Optimization. McCombs Research Paper Series IROM-06-06. McCombs School of Business, Austin (2006)
[92] Lee, G., Tam, N., Yen, N.: Quadratic Programming and Affine Variational Inequalities: A Qualitative Study. Nonconvex Optimization and Its Applications. Springer, Boston (2006)
[93] Li, J., Li, A., Karimi, I.A., Srinivasan, R.: Improving the robustness and efficiency of crude scheduling algorithms. AIChE J. 53(10), 2659-2680 (2007)
[94] Li, J., Misener, R., Floudas, C.A.: Continuous-time modeling and global optimization approach for scheduling of crude oil operations. AIChE J. 58(1), 205-226 (2012)
[95] Li, J., Misener, R., Floudas, C.A.: Scheduling of crude oil operations under demand uncertainty: a robust optimization framework coupled with global optimization. AIChE J. 58(8), 2373-2396 (2012)
[96] Li, X., Armagan, E., Tomasgard, A., Barton, P.I.: Stochastic pooling problem for natural gas production network design and operation under uncertainty. AIChE J. 57(8), 2120-2135 (2011)
[97] Li, X., Tomasgard, A., Barton, P.I.: Decomposition strategy for the stochastic pooling problem. J. Global Optim. 54(4), 765-790 (2012) · Zbl 1282.90141
[98] Lin, X., Floudas, C.A., Kallrath, J.: Global solution approach for a nonconvex MINLP problem in product portfolio optimization. J. Global Optim. 32(3), 417-431 (2005) · Zbl 1098.90098
[99] Lin, Y., Schrage, L.: The global solver in the LINDO API. Optim. Methods Softw. 24(4-5), 657-668 (2009) · Zbl 1177.90325
[100] Loiola, E.M., de Abreu, N.M.M., Boaventura-Netto, P.O., Hahn, P., Querido, T.: A survey for the quadratic assignment problem. Eur. J. Oper. Res. 176(2), 657-690 (2007) · Zbl 1103.90058
[101] Maranas, C.D., Androulakis, I.P., Floudas, C.A., Berger, A.J., Mulvey, J.M.: Solving long-term financial planning problems via global optimization. J. Econ. Dyn. Control 21(8-9), 1405-1425 (1997) · Zbl 0901.90016
[102] Misener, R., Floudas, C.A.: Advances for the pooling problem: modeling, global optimization, and computational studies. Appl. Comput. Math. 8(1), 3-22 (2009) · Zbl 1188.90287
[103] Misener, R., Floudas, C.A.: Global optimization of large-scale pooling problems: quadratically constrained MINLP models. Ind. Eng. Chem. Res. 49(11), 5424-5438 (2010)
[104] Misener, R., Floudas, C.A.: GloMIQO: global mixed-integer quadratic optimizer. J. Global Optim. 57(1), 3-50 (2013) · Zbl 1272.90034
[105] Misener, R., Floudas, C.A.: ANTIGONE: algorithms for continuous/integer global optimization of nonlinear equations. J. Global Optim. 59(2-3), 503-526 (2014) · Zbl 1301.90063
[106] Mouret, S., Grossmann, I.E., Pestiaux, P.: A novel priority-slot based continuous-time formulation for crude-oil scheduling problem. Ind. Eng. Chem. Res. 48(18), 8515-8528 (2009)
[107] Mouret, S., Grossmann, I.E., Pestiaux, P.: A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling. Comput. Chem. Eng. 35(12), 2750-2766 (2011)
[108] Murtagh, B.A., Saunders, M.A.: Large-scale linearly constrained optimization. Math. Program. 14(1), 41-72 (1978) · Zbl 0383.90074
[109] Murtagh, BA; Saunders, MA; Buckley, AG (ed.); Goffin, JL (ed.), A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints, No. 16, 84-117 (1982), Berlin
[110] Neumaier, A.: Complete search in continuous global optimization and constraint satisfaction. Acta Numer. 13, 271-369 (2004) · Zbl 1113.90124
[111] Nyberg, A., Grossmann, I.E., Westerlund, T.: The optimal design of a three-echelon supply chain with inventories under uncertainty (2012). http://www.minlp.org/library/problem/index.php?i=157. Accessed Sept 2017
[112] Papageorgiou, D.J., Toriello, A., Nemhauser, G.L., Savelsbergh, M.W.P.: Fixed-charge transportation with product blending. Transp. Sci. 46(2), 281-295 (2012)
[113] Parpas, P.; Rustem, B.; Gavrilova, M. (ed.); Gervasi, O. (ed.); Kumar, V. (ed.); Tan, C. (ed.); Taniar, D. (ed.); Laganá, A. (ed.); Mun, Y. (ed.); Choo, H. (ed.), Global optimization of the scenario generation and portfolio selection problems, No. 3982, 908-917 (2006), Berlin
[114] Pham, V., Laird, C., El-Halwagi, M.: Convex hull discretization approach to the global optimization of pooling problems. Ind. Eng. Chem. Res. 48(4), 1973-1979 (2009)
[115] Pillo, G.D., Grippo, L., Lampariello, F.: A class of structured quasi-newton algorithms for optimal control problems. IFAC Proc. Vol. 16(8), 101-107 (1983). 4th IFAC Workshop on Applications of Nonlinear Programming to Optimization and Control, San Francisco, CA, USA, 20-21 June 1983
[116] Pintér, JD; Bomze, IM (ed.); Csendes, T. (ed.); Horst, R. (ed.); Pardalos, PM (ed.), LGO: a program system for continuous and Lipschitz global optimization, 183-197 (1997), Boston
[117] Pintér, JD; Leone, R. (ed.); Murli, A. (ed.); Pardalos, PM (ed.); Toraldo, G. (ed.), A model development system for global optimization, 301-314 (1998), Boston
[118] 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. Comput. Chem. Eng. 34(3), 318-330 (2010)
[119] Rebennack, S., Kallrath, J., Pardalos, P.M.: Column enumeration based decomposition techniques for a class of non-convex MINLP problems. J. Global Optim. 43(2-3), 277-297 (2009) · Zbl 1169.90417
[120] Rendl, F., Rinaldi, G., Wiegele, A.: Solving max-cut to optimality by intersecting semidefinite and polyhedral relaxations. Math. Program. 121(2), 307-335 (2008) · Zbl 1184.90118
[121] Rendl, F., Wolkowicz, H.: A semidefinite framework for trust region subproblems with applications to large scale minimization. Math. Program. 77(1), 273-299 (1997) · Zbl 0888.90137
[122] Rios, L.M., Sahinidis, N.V.: Portfolio optimization for wealth-dependent risk preferences. Ann. Oper. Res. 177(1), 63-90 (2010) · Zbl 1195.91148
[123] Rothberg, E.: Solving quadratically-constrained models using Gurobi (2012). http://www.gurobi.com/resources/seminars-and-videos/gurobi-quadratic-constraints-webinar. Accessed Sept 2017
[124] Ruiz, J.P., Grossmann, I.E.: Exploiting vector space properties to strengthen the relaxation of bilinear programs arising in the global optimization of process network. Optim. Lett. 5(1), 1-11 (2011) · Zbl 1211.90186
[125] Ruiz, M., Briant, O., Clochard, J.M., Penz, B.: Large-scale standard pooling problems with constrained pools and fixed demands. J. Global Optim. 56(3), 939-956 (2013) · Zbl 1275.90069
[126] Saif, Y., Elkamel, A., Pritzker, M.: Global optimization of reverse osmosis network for wastewater treatment and minimization. Ind. Eng. Chem. Res. 47(9), 3060-3070 (2008)
[127] Schittkowski, K.: Numerical solution of a time-optimal parabolic boundary-value control problem. J. Optim. Theory Appl. 27(2), 271-290 (1979) · Zbl 0372.49014
[128] Stojanovic, S.: Optimal damping control and nonlinear elliptic systems. SIAM J. Control Optim. 29(3), 594-608 (1991) · Zbl 0742.49017
[129] Szabó, PG; Markót, CM; Csendes, T.; Audet, C. (ed.); Hansen, P. (ed.); Savard, G. (ed.), Global optimization in geometry: circle packing into the square, 233-265 (2005), New York
[130] Tadayon, B., Smith, J.C.: Algorithms for an integer multicommodity network flow problem with node reliability considerations. J. Optim. Theory Appl. 161(2), 506-532 (2013) · Zbl 1291.90280
[131] Tahanan, M., van Ackooij, W., Frangioni, A., Lacalandra, F.: Large-scale unit commitment under uncertainty. 4OR 13(2), 115-171 (2015) · Zbl 1321.90007
[132] Tarski, A.: A decision method for elementary algebra and geometry. Technical Reports R-109, Rand Corporation (1951) · Zbl 0044.25102
[133] Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Nonconvex Optimization and Its Applications, vol. 65. Kluwer Academic Publishers, Alphen aan den Rijn (2002) · Zbl 1031.90022
[134] Tawarmalani, M., Sahinidis, N.V.: Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math. Program. 99(3), 563-591 (2004) · Zbl 1062.90041
[135] Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2), 225-249 (2005) · Zbl 1099.90047
[136] Teles, J.P., Castro, P.M., Matos, H.A.: Global optimization of water networks design using multiparametric disaggregation. Comput. Chem. Eng. 40, 132-147 (2012)
[137] Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J., Martí, R.: Scatter search and local NLP solvers: a multistart framework for global optimization. Informs J. Comput. 19(3), 328-340 (2007) · Zbl 1241.90093
[138] Vavasis, S.: Quadratic programming is in NP. Inf. Process. Lett. 36, 73-77 (1990) · Zbl 0719.90052
[139] Vigerske, S.: MINLPLib 2. In: L.G. Casado, I. García, E.M.T. Hendrix (eds.) Proceedings of the XII Global Optimization Workshop MAGO 2014, pp. 137-140 (2014). http://www.gamsworld.org/minlp/minlplib2
[140] Vigerske, S., Gleixner, A.: SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework. Optim. Methods Softw. 33(3), 563-593 (2018) · Zbl 1398.90112
[141] Viswanathan, J., Grossmann, I.E.: A combined penalty function and outer-approximation method for MINLP optimization. Comput. Chem. Eng. 14(7), 769-782 (1990)
[142] Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25-57 (2006) · Zbl 1134.90542
[143] Westerlund, T., Lundquist, K.: Alpha-ECP, version 5.04. an interactive MINLP-solver based on the extended cutting plane method. Technical Reports 01-178-A. Process Design Laboratory, Åbo Akademi University, Åbo, Finland (2003)
[144] Westerlund, T., Pörn, R.: Solving pseudo-convex mixed integer optimization problems by cutting plane techniques. Optim. Eng. 3(3), 253-280 (2002) · Zbl 1035.90051
[145] Wikipedia: Quadratic programming (2016). https://en.wikipedia.org/wiki/Quadratic_programming. Accessed Sept 2017
[146] Wikipedia: Quadratically constrained quadratic program (2016). https://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program. Accessed Sept 2017
[147] Wright, S.: Primal-Dual Interior-Point Method. SIAM, Philadelphia (1997) · Zbl 0863.65031
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.