Reduced Outer Space Algorithm for Globally Computing Affine Sum-of-Ratios Problems

Abstract

This paper investigates the affine sum-of-ratios problem (SRP) which has numerous applications in many fields of economy and engineering. For globally computing the affine SRP, based on equivalent transformation and new affine relaxation problem, a reduced outer space branch-and-bound algorithm is designed. The designed algorithm has been proven to converge to a global optimal solution of the problem (SRP) eventually. Meanwhile, the maximum iteration time for the algorithm in the worst case is estimated by analyzing its computational complexity. Finally, numerical experimental results indicate that the presented algorithm is robust and effective.