New higher-order weak lower inner epiderivatives and application to Karush–Kuhn–Tucker necessary optimality conditions in set-valued optimization
New higher-order weak lower inner epiderivatives and application to Karush–Kuhn–Tucker necessary optimality conditions in set-valued optimization
复制标题
新的高阶弱下内表皮衍生物及其在集值优化中Karush-Kuhn-Tucker必要最优条件的应用
DOI：
10.1007/s13160-020-00426-y
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发表时间：
2020
影响因子：
0.9
通讯作者：
Yujia Guo
中科院分区：
文献类型：
--
作者：
Zhenhua Peng;Z. Wan;Yujia Guo
本文的目的是建立高阶Karush-Kuhn-Tucker高阶最优性必要条件，其中目标函数和约束函数的导数是分离的。本文首先引入了集值映射的高阶弱下内上表皮导数的概念，并讨论了新上表皮导数的一些有用性质，如凸性、次可加性和链法则。利用这一新概念及其性质，我们建立了高阶Karush-Kuhn-Tucker最优性必要条件，即经典型Karush-Kuhn-Tucker最优性条件，改进和加强了文献中的一些结果.几个例子来说明我们的结果。最后给出了集值优化的弱对偶和强对偶定理。
The purpose of the paper is to establish higher-order Karush–Kuhn–Tucker higher-order necessary optimality conditions for set-valued optimization where the derivatives of objective and constraint functions are separated. We first introduce concepts of higher-order weak lower inner epiderivatives for set-valued maps and discuss some useful properties about new epiderivatives, for instance, convexity, subadditivity and chain rule. With the help of the new concept and its properties, we establish higher-order Karush–Kuhn–Tucker necessary optimality conditions which is the classical type Karush–Kuhn–Tucker optimality conditions and improve and enhance some recent existing results in the literatures. Several examples are provided to illustrate our results. Finally, we provide weak and strong duality theorems in set-valued optimization.