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Nondifferentiable minimax programming problems with applications
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DOI：10.1007/s10479-015-1843-3.png)
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Abstract
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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
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