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A parametric solution method for a generalized fractional programming problem

Author

Listed:
  • YongJin Kim

    (University of Science)

  • YunChol Jong

    (Tianjin University of Technology)

  • JinWon Yu

    (University of Science
    Tianjin University of Technology)

Abstract

This paper proposes a parametric method for solving a generalized fractional programming problem which is called sum-of-ratios problem. The sum-of-ratios problems occur in many fields including computer vision, finance, engineering and management. Compared with other methods based on branch-and-bound procedure, our algorithm is based on Newton-like method for solving a system of nonlinear equations with parameters and it needs to solve convex programming problem in each iteration. We showed the global linear and local superlinear/quadratic rate of convergence of the algorithm. We demonstrated the practical efficiency of the algorithm by numerical experiments for various kinds of sum-of-ratios problem. In the numerical experiments, our method exhibited better solution quality and better convergence rate than other methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00102-y
    DOI: 10.1007/s13226-021-00102-y
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. M. N. Yarahmadi & S. A. MirHassani & F. Hooshmand, 2023. "A heuristic method to find a quick feasible solution based on the ratio programming," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    2. S. M. Mirhadi & S. A. MirHassani, 2022. "A solution approach for cardinality minimization problem based on fractional programming," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 583-602, August.
    3. F. Hooshmand & Z. Rasouli, 2023. "Enhanced index tracking problem: a new optimization model and a sum-of-ratio based algorithm," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1286-1311, September.

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