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Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs

Author

Listed:
  • Bo Zhang

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

  • Yuelin Gao

    (Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China
    Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan 750021, China)

  • Xia Liu

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

  • Xiaoli Huang

    (Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China
    Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan 750021, China)

Abstract

In this paper, a new relaxation bounding method is proposed for a class of linear multiplicative programs. Although the 2 p − 1 variable is introduced in the construction of equivalence problem, the branch process of the algorithm is only carried out in p − dimensional space. In addition, a super-rectangular reduction technique is also given to greatly improve the convergence rate. Furthermore, we construct an output-space branch-and-bound reduction algorithm based on solving a series of linear programming sub-problems, and prove the convergence and computational complexity of the algorithm. Finally, to verify the feasibility and effectiveness of the algorithm, we carried out a series of numerical experiments and analyzed the advantages and disadvantages of the algorithm by numerical results.

Suggested Citation

  • Bo Zhang & Yuelin Gao & Xia Liu & Xiaoli Huang, 2020. "Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs," Mathematics, MDPI, vol. 8(3), pages 1-34, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:315-:d:326742
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    References listed on IDEAS

    as
    1. Maranas, C. D. & Androulakis, I. P. & Floudas, C. A. & Berger, A. J. & Mulvey, J. M., 1997. "Solving long-term financial planning problems via global optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1405-1425, June.
    2. H. P. Benson, 2005. "Decomposition Branch-and-Bound Based Algorithm for Linear Programs with Additional Multiplicative Constraints," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 41-61, July.
    3. H. P. Benson & G. M. Boger, 2000. "Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 301-322, February.
    4. H. P. Benson & G. M. Boger, 1997. "Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 487-510, August.
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    Cited by:

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    2. Gao, YueLin & Zhang, Bo, 2023. "Output-space branch-and-bound reduction algorithm for generalized linear fractional-multiplicative programming problem," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Yaping Deng & Peiping Shen, 2025. "A new branch-and-bound algorithm for generalized affine multiplicative programming," Journal of Global Optimization, Springer, vol. 93(1), pages 87-112, September.

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