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Dual method of centers for solving generalized fractional programs

Author

Listed:
  • K. Boufi

    (Faculté des Sciences et Techniques)

  • A. Roubi

    (Faculté des Sciences et Techniques)

Abstract

In this paper we analyze the method of centers for generalized fractional programs, with further insights. The introduced method is based on a different parametric auxiliary problem than Dinkelbach’s type. With the help of this auxiliary parametric problem, we present a new dual for convex generalized fractional programs. We then propose an algorithm to solve this problem, and subsequently the original primal program. The proposed algorithm generates a sequence of dual values that converges from below to the optimal value. The method also generates a bounded sequence of dual solutions whose every accumulation point is a solution of the dual problem. The rate of convergence is shown to be at least linear. In the penultimate section, we specialize the results obtained for the linear case. The computational results show that the different variants of our algorithms, primal as well as dual, are competitive.

Suggested Citation

  • K. Boufi & A. Roubi, 2017. "Dual method of centers for solving generalized fractional programs," Journal of Global Optimization, Springer, vol. 69(2), pages 387-426, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0523-z
    DOI: 10.1007/s10898-017-0523-z
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    References listed on IDEAS

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    1. M. Gugat, 1998. "Prox-Regularization Methods for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 691-722, December.
    2. A. Roubi, 2000. "Method of Centers for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 123-143, October.
    3. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Karima Boufi & Mostafa El Haffari & Ahmed Roubi, 2020. "Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 105-132, October.
    2. Jiao, Hongwei & Li, Binbin, 2022. "Solving min–max linear fractional programs based on image space branch-and-bound scheme," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Smail Addoune & Karima Boufi & Ahmed Roubi, 2018. "Proximal Bundle Algorithms for Nonlinearly Constrained Convex Minimax Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 212-239, October.
    4. H. Boualam & A. Roubi, 2019. "Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs," Journal of Global Optimization, Springer, vol. 74(2), pages 255-284, June.

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