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Duality in nondifferentiable minimax fractional programming with generalized convexity

Summary: Duality in nondifferentiable minimax fractional
programming with generalized convexity
I. Ahmad *, Z. Husain
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
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.
” 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].


Source: Ahmad, Izahr - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics