Nondifferentiable minimax programming problems with applications
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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.
KeywordsMinimax programming problem Optimality condition Duality Limiting subdifferential \(L\)-invex-infine function
Mathematics Subject Classification49K99 65K10 90C29 90C46
The authors would like to thank the editor and the referees for valuable comments and suggestions.
Conflict of interest
The authors declare that they have no potential conflict of interest.
- Mond, B., & Weir, T. (1981). Generalized concavity and duality. In S. Schaible & W. T. Ziemba (Eds.), Generalized concavity in optimization and economics (pp. 263–279). New York: Academic Press.Google Scholar
- Mordukhovich, B. S. (2006). Variational analysis and generalized differentiation. I: basic theory. Berlin: Springer.Google Scholar