Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 129, No. 2, pp. 255­275, May 2006 ( C 2006)
DOI: 10.1007/s10957-006-9057-0
Optimality Conditions and Duality
in Nondifferentiable Minimax Fractional
Programming with Generalized Convexity1
I. AHMAD2
AND Z. HUSAIN3
Communicated by P. M. Pardalos
Published Online: 6 December 2006
Abstract. We establish sufficient optimality conditions for a class of nondif-
ferentiable minimax fractional programming problems involving (F, , , d)-
convexity. Subsequently, we apply the optimality conditions to formulate two
types of dual problems and prove appropriate duality theorems.
Key Words. Minimax fractional programming, sublinear functionals,
optimality conditions, duality, generalized convexity.
1. Introduction
Schmitendorf (Ref. 1) established necessary and sufficient optimality condi-
tions for a minimax problem. Tanimoto (Ref. 2) applied these optimality conditions
to define a dual problem and derived duality theorems, which were extended for the
fractional analogue of a generalized minimax problem by Yadav and Mukherjee

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

Collections: Mathematics