Effective outcome space branch-and-bound algorithm for solving the sum of affine ratios problem

Author:

Shi Yan1,Zheng Qunzhen2,Yin Jingben3

Affiliation:

1. College of Information Engineering, Henan University of Animal Husbandry and Economy, Zhengzhou 450000, China; wqmshiyan@163.com

2. School of Statistics and Mathematics, Henan Finance University, Zhengzhou 450046, China

3. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Abstract

<p>This paper proposes an efficient method for acquiring the global solution of the sum of affine ratios problem (SARP) in the reduced outer space. Using equivalence conversions, the original problem was transformed into an equivalent problem. Then, an affine relaxation problem of the equivalent problem was constructed by exploiting linearization techniques. Subsequently, an outcome space branch-and-bound algorithm was proposed, the convergence of the algorithm was proved and the computational complexity was estimated. Finally, numerical examples were presented to demonstrate the effectiveness and feasibility of the presented algorithm.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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