New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

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• 作者：Zhenhua Peng ; Yihong Xu
• 关键词：Weak minimizer ; Near cone ; subconvexlikeness ; Set ; valued optimization ; Cone
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：172
• 期：1
• 页码：128-140
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a separation theorem for convex sets, second-order Fritz John and Kuhn–Tucker necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of lower semicontinuous, a second-order Kuhn–Tucker sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem.