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

Author:

Jiao Hongwei1ORCID,Ma Junqiao1ORCID,Shang Youlin2ORCID

Affiliation:

1. School of Mathematical Sciences, Henan Institute of Science and Technology, Hualan Street, Henan, Xinxiang 453003, P. R. China

2. School of Mathematical Sciences, Henan University of Science and Technology, Kaiyuan Street, Henan, Luoyang 471023, P. R. China

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.

Funder

National Natural Science Foundation of China

China Postdoctoral Science Foundation

Key Scientific and Technological Research Projects in Henan

Publisher

World Scientific Pub Co Pte Ltd

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