论文信息 - Comparison of convex relaxations of quadrilinear terms

Comparison of convex relaxations of quadrilinear terms

In this paper we compare four different ways to compute a convex linea r relaxation of a quadrilinear monomial on a box, analyzing their relative tightness. We computation ally compare the quality of the relaxations, and we provide a general theorem on pairwisecomparison of relaxation strength, which applies to some of our pairs of relaxations for quadrilinea r monomials. Our results can be used to configure a spatial Branch-and-Bound global optimizatio n alg rithm. We apply our results to the Molecular Distance Geometry Problem, demonstrating the usef ulness of the present study.

Sonia Cafieri | Leo Liberti | Jon Lee

[1] Leo Liberti,et al. Molecular Distance Geometry Problem , 2009, Encyclopedia of Optimization.

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

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

[4] Leo Liberti,et al. Convex Envelopes of Monomials of Odd Degree , 2003, J. Glob. Optim..

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

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

[7] Edward M. B. Smith,et al. On the optimal design of continuous processes , 1996 .

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

[9] Carlile Lavor,et al. On generating Instances for the Molecular Distance Geometry Problem , 2006 .

[10] Nikolaos V. Sahinidis,et al. Convex extensions and envelopes of lower semi-continuous functions , 2002, Math. Program..

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

[12] Leo Liberti,et al. Reformulation in mathematical programming: An application to quantum chemistry , 2009, Discret. Appl. Math..