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Maximizing the ratio of two convex functions over a convex set

✍ Scribed by Harold P. Benson

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 126 KB
Volume: 53
Category: Article
ISSN: 0894-069X
DOI: 10.1002/nav.20143

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✦ Synopsis

Abstract

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

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