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AIMS Mathematics

2024, Volume 9, Issue 9: 23837-23858. doi: 10.3934/math.20241158
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Research article

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

  • 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
  • Received: 27 April 2024 Revised: 17 July 2024 Accepted: 29 July 2024 Published: 09 August 2024

  • MSC : 90C32, 90C26

  • 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.

    Citation: Yan Shi, Qunzhen Zheng, Jingben Yin. Effective outcome space branch-and-bound algorithm for solving the sum of affine ratios problem[J]. AIMS Mathematics, 2024, 9(9): 23837-23858. doi: 10.3934/math.20241158

    Related Papers:

  • 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.



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  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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