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Solving Sum of Ratios Fractional Programs via Concave Minimization

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  • H. P. Benson

    (University of Florida)

Abstract

This article presents an algorithm for globally solving a sum of ratios fractional programming problem. To solve this problem, the algorithm globally solves an equivalent concave minimization problem via a branch-and-bound search. The main work of the algorithm involves solving a sequence of convex programming problems that differ only in their objective function coefficients. Therefore, to solve efficiently these convex programming problems, an optimal solution to one problem can potentially be used to good advantage as a starting solution to the next problem.

Suggested Citation

  • H. P. Benson, 2007. "Solving Sum of Ratios Fractional Programs via Concave Minimization," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 1-17, October.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:1:d:10.1007_s10957-007-9199-8
    DOI: 10.1007/s10957-007-9199-8
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    References listed on IDEAS

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    1. H. P. Benson, 2004. "On the Global Optimization of Sums of Linear Fractional Functions over a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 19-39, April.
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    Cited by:

    1. Fengqiao Luo & Sanjay Mehrotra, 2021. "A geometric branch and bound method for robust maximization of convex functions," Journal of Global Optimization, Springer, vol. 81(4), pages 835-859, December.
    2. Lin, Yun Hui & Wang, Yuan & He, Dongdong & Lee, Loo Hay, 2020. "Last-mile delivery: Optimal locker location under multinomial logit choice model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    3. Luca Consolini & Marco Locatelli & Jiulin Wang & Yong Xia, 2020. "Efficient local search procedures for quadratic fractional programming problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 201-232, May.
    4. YongJin Kim & YunChol Jong & JinWon Yu, 2021. "A parametric solution method for a generalized fractional programming problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 971-989, December.
    5. Luo, Fengqiao & Mehrotra, Sanjay, 2019. "Decomposition algorithm for distributionally robust optimization using Wasserstein metric with an application to a class of regression models," European Journal of Operational Research, Elsevier, vol. 278(1), pages 20-35.

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