Global optimization for the sum of linear ratios problem over convex feasible region

Abstract

In this paper, a deterministic method is presented for globally solving the sum of linear ratios problem over convex feasible region. The proposed approach is based on the branch and bound scheme. First, by introducing new variables and using concave envelope, the fundamental problems for estimating upper bounds in the branch and bound algorithm change into a sequence of relaxation convex programming problems which have less variables and constraints. Next, a new bounding tightening strategy is proposed to enhance solution produce. Finally, the analysis theory and numerical experiments are reported on the feasibility and efficiency of the proposed algorithm. © 2012 Springer-Verlag.