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On the Global Optimization of Sums of Linear Fractional Functions over a Convex Set

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  • H. P. Benson

    (University of Florida)

Abstract

The global optimization of the sum of linear fractional functions has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are nonconvex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms may be difficult to implement and are usually relatively inaccessible. In this article, we show that, by using suitable transformations, a number of potential and known methods for globally solving these problems become available. These methods are often more accessible and use more standard tools than the customized algorithms proposed to date. They include, for example, parametric convex programming and concave minimization methods.

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  • 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.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026129.07165.5a
    DOI: 10.1023/B:JOTA.0000026129.07165.5a
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    References listed on IDEAS

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    1. H. P. Benson, 2003. "Generating Sum-of-Ratios Test Problems in Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 615-621, December.
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    Cited by:

    1. H. P. Benson, 2010. "Branch-and-Bound Outer Approximation Algorithm for Sum-of-Ratios Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 1-18, July.
    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. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Qingyun Tian & Yun Hui Lin & David Z. W. Wang, 2021. "Autonomous and conventional bus fleet optimization for fixed-route operations considering demand uncertainty," Transportation, Springer, vol. 48(5), pages 2735-2763, October.
    5. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    6. 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.
    7. Ruan, N. & Gao, D.Y., 2015. "Global solutions to fractional programming problem with ratio of nonconvex functions," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 66-72.
    8. Erdogan, Günes & Cordeau, Jean-François & Laporte, Gilbert, 2010. "The Attractive Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 203(1), pages 59-69, May.

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