Date of Original Version

11-2003

Type

Book Chapter

Abstract or Description

We investigate some approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. We assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We provide a survey of disjunctive programming with convex relaxations, logic-based outer approximation, and logic-based Benders decomposition. We then introduce a branch-and-bound method with convex quasi-relaxations (BBCQ) that can be effective when the discrete variables take a large number of real values. The BBCQ method generalizes work of Bollapragada, Ghattas and Hooker on structural design problems. It applies when the constraint functions are concave in the discrete variables and have a weak homogeneity property in the continuous variables.

DOI

10.1007/11425076_4

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Published In

C. Jermann, A. Neumaier, and D. Sam, eds., Global Optimization and Constraint Satisfaction (COCOS 2003, invited talk), LNCS 3478, 46-60.