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Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic

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  • H. P. Benson

    (University of Florida)

  • G. M. Boger

    (University of Florida)

Abstract

Multiplicative programming problems are difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, finance, economics, and other fields. This article has two purposes. The first is to present an analysis that shows several relationships between concave multiplicative programs and concave minimization problems, and between concave multiplicative programs and certain multiple-objective mathematical programs. The second purpose is to propose and report computational results for a heuristic efficient-point search algorithm that we have designed for use on linear multiplicative programming problems. To our knowledge, this is the first heuristic algorithm of its type. The theoretical and algorithmic results given in the article offer some potentially important new avenues for analyzing and solving multiplicative programming problems of various types.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022600232285
    DOI: 10.1023/A:1022600232285
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    References listed on IDEAS

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    1. Gerald W. Evans, 1984. "An Overview of Techniques for Solving Multiobjective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1268-1282, November.
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    Cited by:

    1. T. Kuno, 1999. "Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 121-135, October.
    2. Alberto Caprara & Marco Locatelli & Michele Monaci, 2016. "Theoretical and computational results about optimality-based domain reductions," Computational Optimization and Applications, Springer, vol. 64(2), pages 513-533, June.
    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. 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. 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.
    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. 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.

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