A DC approach for minimax fractional optimization programs with ratios of convex functions. (4th March 2022)

• Record Type: Journal Article
• Authors: Ghazi, A.; Roubi, A.
• Is Part Of: Optimization methods and software. Volume 37:Number 2(2022)
• Page Start: 639
• Page End: 657
• Publication Date: 2022-03-04
• Subjects: Fractional programming -- quotient of convex functions -- difference of convex functions -- optimality conditions -- Dinkelbach algorithms; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1818234
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper deals with minimax fractional programs whose objective functions are the maximum of finite ratios of convex functions, with arbitrary convex constraints set. For such problems, Dinkelbach-type algorithms fail to work since the parametric subproblems may be nonconvex, whereas the latter need a global optimal solution of these subproblems. We give necessary optimality conditions for such problems, by means of convex analysis tools. We then propose a method, based on solving approximately a sequence of parametric convex problems, which acts as dc (difference of convex functions) algorithm, if the parameter is positive and as Dinkelbach algorithm if not. We show that every cluster point of the sequence of optimal solutions of these subproblems satisfies necessary optimality conditions of KKT criticality type, that are also of Clarke stationarity type. Finally we end with some numerical tests to illustrate the behaviour of the algorithm.