Duality in nondifferentiable minimax fractional programming with generalized convexity I. Ahmad * , Z. Husain Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India Abstract A Mond–Weir type dual for a class of nondifferentiable minimax fractional programming problem is considered. Appropriate duality results are proved involving (F, a, q, d)-pseudoconvex functions. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Nondifferentiable minimax programming; Fractional programming; Duality; Generalized convexity 1. Introduction Fractional programming is an interesting subject appeared in many types of optimization problems. For example, it can be used in engineering and economics to minimize a ratio of functions between a given period of time and a utilized resource in order to measure the efficiency or productivity of a system. In these types of problems the objective function is usually given as a ratio of functions in fractional programming form (see Stancu-Minasian [16]). Optimization problems with minimax type functions arise in the design of electronic circuits, however mini- max fractional problems appear in the formulation of discrete and continuous rational approximation problems with respect to the Chebyshev norm [3], in continuous rational games [14], in multiobjective programming [15], in engineering design as well as in some portfolio selection problems discussed by Bajona-xandri and Martinez- legaz [2]. Minimax mathematical programming has been of much interest in the recent past [1,4,5,11,13,18–20]. Schmitendorf [13] established necessary and sufficient optimality conditions for minimax problem. Tanimoto [17] applied these optimality conditions to define a dual problem and derived duality theorems, which were extended for the fractional analogue of generalized minimax problem by Yadav and Mukherjee [19]. Motivated by various concepts of generalized convexity, Liang et al. [8,9] introduced a unified formulation of generalized convexity, which was called (F, a, q, d)-convexity and obtained some corresponding optimality 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.10.002 * Corresponding author. E-mail address: izharamu@hotmail.com (I. Ahmad). Applied Mathematics and Computation 176 (2006) 545–551 www.elsevier.com/locate/amc