Global optimization algorithm for the nonlinearsum of ratios problem

Authors:
H. P. Benson
Affiliations:
Professor, Warrington College of Business Administration, University of Florida, Gainesville, Florida
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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Abstract

This article presents a branch-and-bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm economizes the required computations by conducting the branch-and-bound search in Rp, rather than in Rn, where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of convex programming problems for which standard algorithms are available.