An outcome space approach for generalized convex multiplicative programs

Authors:
Rúbia M. Oliveira;Paulo A. Ferreira
Affiliations:
Department of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande, Brazil 79070-900;Faculty of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil 13083-852
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

This paper addresses the problem of minimizing an arbitrary finite sum of products of two convex functions over a convex set. Nonconvex problems in this form constitute a class of generalized convex multiplicative problems. Convex analysis results allow to reformulate the problem as an indefinite quadratic problem with infinitely many linear constraints. Special properties of the quadratic problem combined with an adequate outer approximation procedure for handling its semi-infinite constrained set enable an efficient constraint enumeration global optimization algorithm for generalized convex multiplicative programs. Computational experiences illustrate the proposed approach.