Global Optimization of Nonlinear Sums of Ratios

Author: Benson H.P.

Source: Journal of Mathematical Analysis and Applications, Volume 263, Number 1, November 2001 , pp. 301-315(15)

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Abstract:

The nonlinear sum of ratios problem (P) has several important applications. However, it is also a difficult problem to solve, since it generally possesses many local optima that are not global optima. In this article we present and show the convergence of an algorithm for finding a global optimal solution to problem (P). The algorithm uses a branch and bound search procedure that globally solves problem (P) by concentrating primarily on solving an equivalent outcome space version of the problem. The algorithm can be implemented by using standard convex programming methods. Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: Warrington College of Business Administration, University of Florida, Gainesville, Florida, 32611-7169

Publication date: 2001-11-01