New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems
Citation
Li, S.J. and Zhu, S.K. and Teo, K.L. 2012. New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems. Journal of Optimization Theory and Applications 152: pp. 587-604.
Source Title
Journal of Optimization Theory and Applications
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Abstract
In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessary optimality condition for set-valued optimization problems, which is a generalization of the corresponding results in the literature.
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