Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions
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 frac...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 187; H. 1; S. 105 - 132 |
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| 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. |
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| AbstractList | 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. |
| Author | El Haffari, Mostafa Roubi, Ahmed Boufi, Karima |
| Author_xml | – sequence: 1 givenname: Karima surname: Boufi fullname: Boufi, Karima organization: Laboratoire MISI, Faculté des Sciences et Techniques, Univ. Hassan 1 – sequence: 2 givenname: Mostafa surname: El Haffari fullname: El Haffari, Mostafa organization: Laboratoire MISI & Ecole Normale Supérieure, Univ. Abdelmalek Essaâdi – sequence: 3 givenname: Ahmed surname: Roubi fullname: Roubi, Ahmed email: roubia@hotmail.com organization: Laboratoire MISI, Faculté des Sciences et Techniques, Univ. Hassan 1 |
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| CitedBy_id | crossref_primary_10_1007_s12190_025_02427_x crossref_primary_10_1007_s12190_025_02609_7 crossref_primary_10_1016_j_chaos_2022_112682 crossref_primary_10_1142_S0217595923500367 crossref_primary_10_1007_s11590_020_01694_w crossref_primary_10_1051_ro_2025063 |
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| Keywords | Optimality conditions 90C32 90C46 90C25 90C47 Difference of convex functions Method of centers 90C26 Fractional programming |
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| Title | Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions |
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