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Global Maximization of a Generalized Concave Multiplicative Function

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  • H. P. Benson

    (University of Florida)

Abstract

This article presents a branch-and-bound algorithm for globally solving the problem (P) of maximizing a generalized concave multiplicative function over a compact convex set. Since problem (P) does not seem to have been studied previously, the algorithm is apparently the first algorithm to be proposed for solving this problem. It works by globally solving a problem (P1) equivalent to problem (P). The branch-and-bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of problem (P) belong. Convergence of the algorithm is shown; computational considerations and benefits for users of the algorithm are given. A sample problem is also solved.

Suggested Citation

  • H. P. Benson, 2008. "Global Maximization of a Generalized Concave Multiplicative Function," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 105-120, April.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9323-9
    DOI: 10.1007/s10957-007-9323-9
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    References listed on IDEAS

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    1. M. Raghavachari, 1969. "On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints," Operations Research, INFORMS, vol. 17(4), pages 680-684, August.
    2. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
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    Cited by:

    1. Alireza M. Ashtiani & Paulo A. V. Ferreira, 2011. "On the Solution of Generalized Multiplicative Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 411-419, May.
    2. 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.
    3. Rúbia Oliveira & Paulo Ferreira, 2010. "An outcome space approach for generalized convex multiplicative programs," Journal of Global Optimization, Springer, vol. 47(1), pages 107-118, May.
    4. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.

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