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An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems

Author

Listed:
  • Hongwei Jiao

    (Henan Institute of Science and Technology)

  • Binbin Li

    (Henan Institute of Science and Technology)

  • Youlin Shang

    (Henan University of Science and Technology)

Abstract

This paper aims to globally solve a generalized affine fractional program problem (GAFPP). Firstly, by introducing some outer space variables and performing equivalent transformations, we can derive the equivalence problem (EP) of the GAFPP. Secondly, by constructing a novel linear relaxation method, we can deduce the affine relaxation problem (ARP) of the EP. Next, by solving the ARP to compute the lower bound, we propose a new outer space branch-and-bound algorithm for tackling the GAFPP. Then, the global convergence of the algorithm is proved, and the computational complexity of the algorithm in the worst case is analyzed. Finally, numerical experimental results are reported to illustrate the effectiveness of the algorithm.

Suggested Citation

  • Hongwei Jiao & Binbin Li & Youlin Shang, 2024. "An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 1-35, April.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:1:d:10.1007_s10957-023-02368-0
    DOI: 10.1007/s10957-023-02368-0
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    References listed on IDEAS

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    2. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    3. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    4. Jiao, Hongwei & Li, Binbin, 2022. "Solving min–max linear fractional programs based on image space branch-and-bound scheme," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Nesterov, Y. & Nemirovskii, A., 1995. "An interior-point method for generalized linear-fractional programming," LIDAM Reprints CORE 1168, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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