Nondifferentiable minimax programming problems with applications

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...

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Bibliographic Details
Published in:Annals of operations research Vol. 251; no. 1-2; pp. 73 - 87
Main Authors: Chuong, Thai Doan, Kim, Do Sang
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2017
Springer
Springer Nature B.V
Subjects:
Applied mathematics
Business and Management
Combinatorics
Differentiation
Inequalities
Mathematical functions
Mathematical programming
Minimax technique
Multiple objective analysis
Operations research
Operations Research/Decision Theory
Optimization
Programming
Studies
Texts
Theory of Computation
49K99
Limiting subdifferential
90C46
Minimax programming problem
Optimality condition
65K10
90C29
Duality
invex-infine function
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-015-1843-3