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Second-order optimality conditions in set optimization. (English) Zbl 1071.49015

Summary: In this paper, we propose second-order epiderivatives for set-valued maps. By using these concepts, second-order necessary optimality conditions and a sufficient optimality condition are given in set optimization. These conditions extend some known results in optimization.

MSC:

49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
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[7] Cambini A. and Martein L. First and Second Order Optimality Conditions in Vector Optimization Preprint Department of Statistics and Applied Mathematics University of Pisa 2000. · Zbl 1012.49022
[14] Luc D.T. Theory of Vector Optimization Lecture Notes in Economics and Mathematical Sciences Springer Berlin Germany Vol. 319 1988.
[20] Mordukhovich B.S. Sensitivity Analysis in Nonsmooth Optimization Theoretical Aspects of Industrial Design Edited by D. A. Filed and V. Komkov SIAM Proceedings in Applied Mathematics Vol. 58 pp. 32-46 1992. · Zbl 0769.90075
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