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

Author

Listed:
  • Bo Zhang

    (North Minzu University
    Ningxia University)

  • Hongyu Wang

    (Ningxia University)

  • Yuelin Gao

    (North Minzu University)

Abstract

In this study, we investigate a class of linear multiplicative programs with positive exponents. By introducing p additional variables, the original problem is reformulated into an equivalent problem (EP) within the output space. Subsequently, a novel global optimization algorithm is introduced to tackle EP. The algorithm primarily leverages two key techniques. One is the outer approximation technique, which tightens the relaxed feasible region of EP and improves the upper bound by carefully examining suitable feasible points. The other is the branch and bound technique to guarantee the global optimality of the solution. Numerical results confirm the effectiveness and practicality of the proposed algorithm, thereby underscoring its potential for real-world applications.

Suggested Citation

  • Bo Zhang & Hongyu Wang & Yuelin Gao, 2024. "Output-Space Outer Approximation Branch-and-Bound Algorithm for a Class of Linear Multiplicative Programs," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 997-1026, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02461-y
    DOI: 10.1007/s10957-024-02461-y
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    References listed on IDEAS

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    1. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    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. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    4. 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.
    5. 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.
    6. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
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