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J Optim Theory Appl (2009) 141: 112 DOI 10.1007/s10957-008-9474-3

Summary: J Optim Theory Appl (2009) 141: 112
DOI 10.1007/s10957-008-9474-3
Higher-Order Duality in Nondifferentiable Minimax
Programming with Generalized Type I Functions
I. Ahmad Z. Husain S. Sharma
Published online: 17 December 2008
Springer Science+Business Media, LLC 2008
Abstract A unified higher-order dual for a nondifferentiable minimax programming
problem is formulated. Weak, strong and strict converse duality theorems are dis-
cussed involving generalized higher-order (F,,,d)-Type I functions.
Keywords Nondifferentiable programming Minimax programming Higher-order
1 Introduction
Several authors have shown their interest in developing optimality conditions and du-
ality results for minimax programming problems. Schmitendorf (Ref. [1]) considered
the following minimax programming problem:
(P) Min sup
f (x,y),
s.t. g(x) 0, x Rn


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


Collections: Mathematics