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Convex programming methods for global optimization (2003)
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| Venue: | in COCOS |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Hooker03convexprogramming,
author = {J. N. Hooker},
title = {Convex programming methods for global optimization},
booktitle = {in COCOS},
year = {2003}
}
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Abstract
Abstract. 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. We address global optimization problems that become convex when selected variables are fixed. If these variables are discrete, the constraints can be reformulated
Keyphrases
global optimization discrete variable convex nonlinear programming method convex quasi-relaxations branch-and-bound method weak homogeneity property bbcq method logic-based outer approximation selected variable structural design problem constraint function logic-based bender decomposition global optimization problem large number continuous variable disjunctive programming convex relaxation nonconvex global optimization problem real value
