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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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 187; no. 1; pp. 105 - 132
Main Authors: Boufi, Karima, El Haffari, Mostafa, Roubi, Ahmed
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2020
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convex analysis
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Operations Research/Decision Theory
Optimization
Theory of Computation
Optimality conditions
90C32
90C46
90C25
90C47
Difference of convex functions
Method of centers
90C26
Fractional programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01738-2