Quantifying Double McCormick
Published Online:6 Jun 2017https://doi.org/10.1287/moor.2017.0846
References
- (1998) A global optimization method, αBB, for general twice-differentiable constrained NLPs: I. Theoretical advances. Comput. Chemical Engrg. 22(9):1137–1158.Crossref, Google Scholar
- (2015) Global optimization of nonconvex problems with multilinear intermediates. Math. Programming Comput. 7(1):1–37.Crossref, Google Scholar
- (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods and Software 24(4–5):597–634.Crossref, Google Scholar
- (2010) On convex relaxations of quadrilinear terms. J. Global Optim. 47(4):661–685.Crossref, Google Scholar
- (2012) Relaxations of multilinear convex envelopes: Dual is better than primal. Klasing R, ed. Experimental Algorithms, Lecture Notes in Computer Science, Vol. 7276 (Springer, Berlin), 87–98.Crossref, Google Scholar
- (2003) Convex Polytopes, 2nd ed. (Springer, New York).Crossref, Google Scholar
- (2008) The convex envelope of (n–1)-convex functions. SIAM J. Optim. 19(3):1451–1466.Crossref, Google Scholar
- (1997) The volume of relaxed Boolean-quadric and cut polytopes. Discrete Math. 163(1–3):293–298.Crossref, Google Scholar
- (2007) Mixed integer nonlinear programming: Some modeling and solution issues. IBM J. Res. Development 51(3/4):489–497.Crossref, Google Scholar
- (1994) Geometric comparison of combinatorial polytopes. Discrete Appl. Math. 55(2):163–182.Crossref, Google Scholar
- (2016) Solving chance-constrained optimization problems with stochastic quadratic inequalities. Oper. Res. 64(4):939–957.Link, Google Scholar
- (2010) The reformulation-optimization software engine. Fukuda K, Hoeven J, Joswig M, Takayama N, eds. Mathematical Software—ICMS 2010, Lecture Notes in Computer Science, Vol. 6327 (Springer, Berlin), 303–314.Crossref, Google Scholar
- (2009) Reformulations in mathematical programming: A computational approach. Abraham A, Hassanien A-E, Siarry P, Engelbrecht A, eds. Foundations of Computational Intelligence Volume 3, Studies in Computational Intelligence, Vol. 203 (Springer, Berlin), 153–234.Crossref, Google Scholar
- (2012) Some results on the strength of relaxations of multilinear functions. Math. Programming, Ser. B 136(2):325–351.Crossref, Google Scholar
- (1976) Computability of global solutions to factorable nonconvex programs: Part I. Convex underestimating problems. Math. Programming 10(1):147–175.Crossref, Google Scholar
- (2004) Trilinear monomials with mixed sign domains: Facets of the convex and concave envelopes. J. Global Optim. 29(2):125–155.Crossref, Google Scholar
- (2004) Trilinear monomials with positive or negative domains: Facets of the convex and concave envelopes. Floudas CA, Pardalos P, eds. Frontiers in Global Optim. (Springer, Boston), 327–352.Crossref, Google Scholar
- (2005) Convex envelopes for edge-concave functions. Math. Programming, Ser. B 103(2):207–224.Crossref, Google Scholar
- (1997) A convex envelope formula for multilinear functions. J. Global Optim. 10(4):425–437.Crossref, Google Scholar
- (1996) A branch-and-reduce approach to global optimization. J. Global Optim. 8(2):107–138.Crossref, Google Scholar
- (2001) Analysis of bounds for multilinear functions. J. Global Optim. 19(4):403–424.Crossref, Google Scholar
- (2005) Interval analysis on directed acyclic graphs for global optimization. J. Global Optim. 33(4):541–562.Crossref, Google Scholar
- (1993) Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications, Vol. 44 (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2014) Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications, Expanded ed., Vol. 151 (Cambridge University Press, Cambridge, UK).Google Scholar
- (1999) A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Comput. Chemical Engrg. 23:457–478.Crossref, Google Scholar
- (2016) On sBB branching for trilinear monomials. Rocha AMAC, Costa MFP, Fernandes EMGP, eds. Proc. XIII Global Optimization Workshop, GOW ’16, 81–84.Google Scholar
- (2017) Experimental validation of volume-based comparison for double-McCormick relaxations. Salvagnin D, Lombardi M, eds. Proc. 14th Internat. Conf. Integration Artificial Intelligence Oper. Res. Techniques Constraint Programming, CPAIOR, Lecture Notes in Computer Science. Forthcoming.Crossref, Google Scholar
- (1994) A decomposition of 2-weak vertex-packing polytopes. Discrete Computational Geometry 12(4):465–479.Crossref, Google Scholar
- (2009) Interval propagation and search on directed acyclic graphs for numerical constraint solving. Computational Optim. Appl. 45(4):499–531.Google Scholar

