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Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions

Author

Listed:
  • Karima Boufi

    (Univ. Hassan 1)

  • Mostafa El Haffari

    (Univ. Abdelmalek Essaâdi)

  • Ahmed Roubi

    (Univ. Hassan 1)

Abstract

We are concerned in this paper with minimax fractional programs whose objective functions are the maximum of finite ratios of difference of convex functions, with constraints also described by difference of convex functions. Like Dinkelbach-type algorithms, the method of centers for generalized fractional programs fails to work for such problems, since the parametric subproblems may be nonconvex, whereas the latters need a global optimal solution for these subproblems. We first give necessary optimality conditions for these problems, by means of convex analysis tools, and then extend the last method to solve such programs. The method is based on solving a sequence of parametric convex problems. We show that every cluster point of the sequence of optimal solutions of these subproblems satisfies necessary optimality conditions of Karush–Kuhn–Tucker criticality type.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:1:d:10.1007_s10957-020-01738-2
    DOI: 10.1007/s10957-020-01738-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    5. A. Roubi, 2000. "Method of Centers for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 123-143, October.
    6. Jian Lv & Li-Ping Pang & Fan-Yun Meng, 2018. "A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information," Journal of Global Optimization, Springer, vol. 70(3), pages 517-549, March.
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    Cited by:

    1. 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).

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