Mathematical Programming

, Volume 136, Issue 1, pp 155–182 | Cite as

Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

Full Length Paper Series B

Abstract

We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to \({\epsilon}\) -global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib.htm).

Mathematics Subject Classification

90C26 Global optimization 90C20 Quadratic programming 90C57 Polyhedral combinatorics; branch & bound 

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© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.Department of Chemical and Biological EngineeringPrinceton UniversityPrincetonUSA

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