Volumetric Guidance for Handling Triple Products in Spatial Branch-and-Bound

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[1]  A. Neumaier,et al.  A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances , 1998 .

[2]  Margaret Wright.  Mathematical Research Challenges in Optimization of Complex Systems , 2006 .

[3]  Jon Lee,et al.  Mixed-integer nonlinear programming: Some modeling and solution issues , 2007, IBM J. Res. Dev..

[4]  François Margot,et al.  Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities , 2016, Oper. Res..

[5]  Edward M. B. Smith,et al.  Global optimisation of nonconvex MINLPs , 1997 .

[6]  Sonia Cafieri,et al.  The Reformulation-Optimization Software Engine , 2010, ICMS.

[7]  Armin Fügenschuh,et al.  Mixed-Integer Nonlinear Problems in Transportation Applications , 2010 .

[8]  Sonia Cafieri,et al.  Reformulations in Mathematical Programming: A Computational Approach , 2009, Foundations of Computational Intelligence.

[9]  Nikolaos V. Sahinidis,et al.  A branch-and-reduce approach to global optimization , 1996, J. Glob. Optim..

[10]  Ambros M. Gleixner,et al.  SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework , 2018, Optim. Methods Softw..

[11]  James E. Falk,et al.  Jointly Constrained Biconvex Programming , 1983, Math. Oper. Res..

[12]  Oktay Günlük,et al.  Perspective Relaxation of Mixed Integer Nonlinear Programs with Indicator Variables , 2008, IPCO.

[13]  Mustafa Mamat,et al.  Performance Profile Comparison Using Matlab , 2015 .

[14]  Richard P. Stanley,et al.  Two poset polytopes , 1986, Discret. Comput. Geom..

[15]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

[16]  R. Boorstyn,et al.  Large-Scale Network Topological Optimization , 1977, IEEE Trans. Commun..

[17]  Hermann Schichl,et al.  Interval Analysis on Directed Acyclic Graphs for Global Optimization , 2005, J. Glob. Optim..

[18]  Harsha Nagarajan,et al.  Tightening McCormick Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning , 2016, CP.

[19]  Anatoliy D. Rikun,et al.  A Convex Envelope Formula for Multilinear Functions , 1997, J. Glob. Optim..

[20]  Alan E. Rosenbluth,et al.  Optimum mask and source patterns to print a given shape , 2002 .

[21]  Robert Weismantel,et al.  The Convex Envelope of (n--1)-Convex Functions , 2008, SIAM J. Optim..

[22]  Sonia Cafieri,et al.  On convex relaxations of quadrilinear terms , 2010, J. Glob. Optim..

[23]  Sinan Gürel,et al.  A strong conic quadratic reformulation for machine-job assignment with controllable processing times , 2009, Oper. Res. Lett..

[24]  R. Tyrrell Rockafellar,et al.  Lagrange Multipliers and Optimality , 1993, SIAM Rev..

[25]  Mohamed Omar,et al.  On Volumes of Permutation Polytopes , 2013 .

[26]  Michael Sagraloff,et al.  On the complexity of the Descartes method when using approximate arithmetic , 2014, J. Symb. Comput..

[27]  Federico Ardila,et al.  Matroid Polytopes and their Volumes , 2010, Discret. Comput. Geom..

[28]  André F. Perold,et al.  Large-Scale Portfolio Optimization , 1984 .

[29]  James R. Luedtke,et al.  Some results on the strength of relaxations of multilinear functions , 2012, Math. Program..

[30]  Christodoulos A. Floudas,et al.  Convex envelopes for edge-concave functions , 2005, Math. Program..

[31]  R. Schneider.  Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[32]  Christodoulos A. Floudas,et al.  Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes , 2004, J. Glob. Optim..

[33]  Nikolaos V. Sahinidis,et al.  Global optimization of nonconvex problems with multilinear intermediates , 2015, Math. Program. Comput..

[34]  Peter Winkler,et al.  Counting linear extensions is #P-complete , 1991, STOC '91.

[35]  Marco Molinaro,et al.  Approximating polyhedra with sparse inequalities , 2015, Math. Program..

[36]  Leo Liberti,et al.  Relaxations of Multilinear Convex Envelopes: Dual Is Better Than Primal , 2012, SEA.

[37]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[38]  Oktay Günlük,et al.  IBM Research Report MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL , 2007 .

[39]  Nikolaos V. Sahinidis,et al.  Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming , 2002 .

[40]  Hermann Schichl,et al.  Interval propagation and search on directed acyclic graphs for numerical constraint solving , 2009, J. Glob. Optim..

[41]  Christodoulos A. Floudas,et al.  GloMIQO: Global mixed-integer quadratic optimizer , 2012, Journal of Global Optimization.

[42]  Christodoulos A. Floudas,et al.  ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations , 2014, Journal of Global Optimization.

[43]  Jon Lee,et al.  The volume of relaxed Boolean-quadric and cut polytopes , 1997, Discret. Math..

[44]  Martin E. Dyer,et al.  A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies , 1989, STOC.

[45]  Adam N. Letchford,et al.  Non-convex mixed-integer nonlinear programming: A survey , 2012 .

[46]  Han Yu,et al.  Experimental Validation of Volume-Based Comparison for Double-McCormick Relaxations , 2017, CPAIOR.

[47]  Christodoulos A. Floudas,et al.  ADVANCES FOR THE POOLING PROBLEM: MODELING, GLOBAL OPTIMIZATION, AND COMPUTATIONAL STUDIES , 2009 .

[48]  Jon Lee,et al.  Quantifying Double McCormick , 2017, Math. Oper. Res..

[49]  Nikolaos V. Sahinidis,et al.  Analysis of Bounds for Multilinear Functions , 2001, J. Glob. Optim..

[50]  Jon Lee,et al.  Geometric Comparison of Combinatorial Polytopes , 1994, Discret. Appl. Math..

[51]  Christodoulos A. Floudas,et al.  Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes , 2004 .

[52]  E. Steigrímsson,et al.  A decomposition of 2-weak vertex-packing polytopes , 1994, Discret. Comput. Geom..

[53]  P. I. Barton,et al.  Stochastic pooling problem for natural gas production network design and operation under uncertainty , 2011 .

[54]  B. Grünbaum,et al.  An enumeration of simplicial 4-polytopes with 8 vertices , 1967 .

[55]  Leo Liberti,et al.  Branching and bounds tighteningtechniques for non-convex MINLP , 2009, Optim. Methods Softw..