Nondifferentiable minimax programming problems with applications

Thai Doan Chuong () and Do Sang Kim ()
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Thai Doan Chuong: Saigon University
Do Sang Kim: Pukyong National University

Annals of Operations Research, 2017, vol. 251, issue 1, No 5, 73-87

Abstract: 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 $$L$$ 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; $$L$$ L -invex-infine function; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-015-1843-3

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