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AIMS Mathematics

2024, Volume 9, Issue 6: 16376-16391. doi: 10.3934/math.2024793
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Research article

Global optimization algorithm for a class of linear ratios optimization problem

  • 1.
    School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
  • 2.
    School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • 3.
    Center for Applied Mathematics of Henan Province, Henan University, Zhengzhou 450046, China
  • 4.
    School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
  • Received: 31 December 2023 Revised: 26 March 2024 Accepted: 17 April 2024 Published: 09 May 2024

  • MSC : 90C26, 90C32

  • We presented an image space branch-and-bound algorithm for globally minimizing the sum of linear ratios problem. In the algorithm, a new linearizing technique was proposed for deriving the linear relaxation problem. An image space region reduction technique was constructed for improving the convergence speed of the algorithm. Moreover, by analyzing the computational complexity of the algorithm, the maximum iterations of the algorithm were estimated, and numerical experimental results showed the potential computing benefits of the algorithm. Finally, a practical application problem in education investment was solved to verify the usefulness of the proposed algorithm.

    Citation: Hongwu Li, Longfei Wang, Yingfeng Zhao. Global optimization algorithm for a class of linear ratios optimization problem[J]. AIMS Mathematics, 2024, 9(6): 16376-16391. doi: 10.3934/math.2024793

    Related Papers:

  • We presented an image space branch-and-bound algorithm for globally minimizing the sum of linear ratios problem. In the algorithm, a new linearizing technique was proposed for deriving the linear relaxation problem. An image space region reduction technique was constructed for improving the convergence speed of the algorithm. Moreover, by analyzing the computational complexity of the algorithm, the maximum iterations of the algorithm were estimated, and numerical experimental results showed the potential computing benefits of the algorithm. Finally, a practical application problem in education investment was solved to verify the usefulness of the proposed algorithm.


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