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Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem

Author

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  • H. P. Benson

    (University of Florida)

Abstract

This article presents a branch-and-bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm economizes the required computations by conducting the branch-and-bound search in ℛp, rather than in ℛn, where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of convex programming problems for which standard algorithms are available.

Suggested Citation

  • H. P. Benson, 2002. "Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 1-29, January.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:1:d:10.1023_a:1013072027218
    DOI: 10.1023/A:1013072027218
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    Citations

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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. Kexin Yin & Xiao Fang & Bintong Chen & Olivia R. Liu Sheng, 2023. "Diversity Preference-Aware Link Recommendation for Online Social Networks," Information Systems Research, INFORMS, vol. 34(4), pages 1398-1414, December.
    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. Peiping Shen & Yuan Ma & Yongqiang Chen, 2011. "Global optimization for the generalized polynomial sum of ratios problem," Journal of Global Optimization, Springer, vol. 50(3), pages 439-455, July.
    5. Gruzdeva, Tatiana V. & Strekalovsky, Alexander S., 2018. "On solving the sum-of-ratios problem," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 260-269.
    6. Ashtiani, Alireza M. & Ferreira, Paulo A.V., 2015. "A branch-and-cut algorithm for a class of sum-of-ratios problems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 596-608.
    7. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    8. Takahito Kuno & Toshiyuki Masaki, 2013. "A practical but rigorous approach to sum-of-ratios optimization in geometric applications," Computational Optimization and Applications, Springer, vol. 54(1), pages 93-109, January.
    9. 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.
    10. 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.
    11. J.-Y. Lin & S. Schaible & R.-L. Sheu, 2010. "Minimization of Isotonic Functions Composed of Fractions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 581-601, September.
    12. Dey, Shibshankar & Kim, Cheolmin & Mehrotra, Sanjay, 2024. "An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation," European Journal of Operational Research, Elsevier, vol. 315(3), pages 980-990.
    13. Mirjam Dür & Charoenchai Khompatraporn & Zelda Zabinsky, 2007. "Solving fractional problems with dynamic multistart improving hit-and-run," Annals of Operations Research, Springer, vol. 156(1), pages 25-44, December.

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