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Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming

Author

Listed:
  • H. P. Benson

    (University of Florida)

  • G. M. Boger

    (University of Florida)

Abstract

This article presents an outcome-space pure cutting-plane algorithm for globally solving the linear multiplicative programming problem. The framework of the algorithm is taken from a pure cutting-plane decision set-based method developed by Horst and Tuy for solving concave minimization problems. By adapting this method to an outcome-space reformulation of the linear multiplicative programming problem, rather than applying directly the method to the original decision-set formulation, it is expected that considerable computational savings can be obtained. Also, we show how additional computational benefits might be obtained by implementing the new algorithm appropriately. To illustrate the new algorithm, we apply it to the solution of a sample problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:2:d:10.1023_a:1004657629105
    DOI: 10.1023/A:1004657629105
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    References listed on IDEAS

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    1. 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:

    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. Boddiford, Ashley N. & Kaufman, Daniel E. & Skipper, Daphne E. & Uhan, Nelson A., 2023. "Approximating a linear multiplicative objective in watershed management optimization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 547-561.
    3. Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
    4. 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.
    5. Yunchol Jong & Yongjin Kim & Hyonchol Kim, 2024. "A method based on parametric convex programming for solving convex multiplicative programming problem," Journal of Global Optimization, Springer, vol. 90(3), pages 573-592, November.
    6. 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).
    7. Daniele Depetrini & Marco Locatelli, 2009. "A FPTAS for a class of linear multiplicative problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 275-288, November.
    8. Mustapha El Moudden & Ahmed El Ghali, 2018. "A new reduced gradient method for solving linearly constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 719-741, December.

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