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Continuous Optimization Minimax mixed integer symmetric duality

Summary: Continuous Optimization
Minimax mixed integer symmetric duality
for multiobjective variational problems
I. Ahmad *, Z. Husain
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
Received 3 June 2004; accepted 22 June 2005
Available online 15 February 2006
A Mond≠Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formu-
lated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse dual-
ity theorems are established. Self duality theorem is proved. A close relationship between these variational problems
and static symmetric dual minimax mixed integer multiobjective programming problems is also presented.
” 2006 Elsevier B.V. All rights reserved.
Keywords: Multiobjective symmetric duality; Variational problem; Mixed integer programming; Efficient solutions; Generalized
1. Introduction
The concept of symmetric duality was introduced and developed by Dorn [8] and Dantzig et al. [6]. Baz-
araa and Goode [2] generalized the results in [6] to arbitrary cones. Mond and Weir [19] presented two pairs
of symmetric duals multiobjective programming problems for efficient solutions and established appropri-
ate duality results with the nonnegative orthant as the cone. Nanda and Das [20] presented the symmetric


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


Collections: Mathematics