Annals of Operations Research

, Volume 251, Issue 1–2, pp 73–87 | Cite as

Nondifferentiable minimax programming problems with applications

Article

Abstract

This paper is devoted to the study of optimality conditions and duality in nondifferentiable minimax programming problems and applications. Employing some advanced tools of variational analysis and generalized differentiation, we establish new necessary conditions for optimal solutions of a minimax programming problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions to the considered problem are also obtained by way of \(L\)-invex-infine functions. We state a dual problem to the primal one and explore weak, strong and converse duality relations between them. In addition, some of these results are applied to a nondifferentiable multiobjective optimization problem.

Keywords

Minimax programming problem Optimality condition Duality Limiting subdifferential \(L\)-invex-infine function 

Mathematics Subject Classification

49K99 65K10 90C29 90C46 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and ApplicationsSaigon UniversityHo Chi Minh CityVietnam
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanKorea

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