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Decomposition Branch-and-Bound Based Algorithm for Linear Programs with Additional Multiplicative Constraints

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  • H. P. Benson

    (University of Florida)

Abstract

This article presents an algorithm for globally solving a linear program (P) that contains several additional multiterm multiplicative constraints. To our knowledge, this is the first algorithm proposed to date for globally solving Problem (P). The algorithm decomposes the problem to obtain a master problem of low rank. To solve the master problem, the algorithm uses a branch-and-bound scheme where Lagrange duality theory is used to obtain the lower bounds. As a result, the lower-bounding subproblems in the algorithm are ordinary linear programs. Convergence of the algorithm is shown and a solved sample problem is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:1:d:10.1007_s10957-005-2655-4
    DOI: 10.1007/s10957-005-2655-4
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    Cited by:

    1. Hongwei Jiao & Binbin Li & Wenqiang Yang, 2024. "A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems," Journal of Global Optimization, Springer, vol. 89(3), pages 597-632, July.
    2. 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.
    3. 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).
    4. 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.
    5. Benson, Harold P. & Sun, Erjiang, 2009. "Branch-and-reduce algorithm for convex programs with additional multiplicative constraints," European Journal of Operational Research, Elsevier, vol. 199(1), pages 1-8, November.

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