New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems
New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems
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新的广义二阶或然表导数和集值优化问题
DOI：
10.1007/s10957-011-9915-2
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发表时间：
2012-03-01
影响因子：
1.9
通讯作者：
Teo, K. L.
中科院分区：
文献类型：
--
作者：
Li, S. J.;Zhu, S. K.;Teo, K. L.
本文引入了集值映射的广义二阶组合相依上图导数的概念，并讨论了它与广义二阶相依上图导数的关系。我们还研究了它的一些性质。然后，利用广义二阶组合相依上导数，建立了集值优化问题的一个统一的二阶最优性充要条件，推广了文献中的相应结果.
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.