 
Summary: 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 MondWeir 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
StancuMinasian [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 Bajonaxandri and Martinez
legaz [2].
