Maximizing the ratio of two convex functions over a convex set

Maximizing the ratio of two convex functions over a convex set

0.00 Avg rating0 Votes
Article ID: iaor20073073
Country: United States
Volume: 53
Issue: 4
Start Page Number: 309
End Page Number: 317
Publication Date: Jun 2006
Journal: Naval Research Logistics
Authors:
Keywords: programming: fractional
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.

Reviews

Required fields are marked *. Your email address will not be published.