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April  2019, 15(2): 465-480. doi: 10.3934/jimo.2018051

## Higher-order weak radial epiderivatives and non-convex set-valued optimization problems

 a. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China b. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

1 Corresponding author.

Received  July 2017 Revised  December 2017 Published  April 2018

Fund Project: This research was partially supported by Chongqing Natural Science Foundation Project of CQ CSTC(Nos. 2015jcyjA30009, 2015jcyjBX0131,2017jcyjAX0382), the Program of Chongqing Innovation Team Project in University (No. CXTDX201601022) and the National Natural Science Foundation of China (No. 11571055).

In the paper, we propose the notion of the higher-order weak radial epiderivative of a set-valued map, and discuss some of its properties. Then, by virtue of the higher-order weak radial epiderivative, we establish the optimality necessary conditions and sufficient ones of weak efficient solutions (Pareto efficient solutions) for non-convex set-valued optimization problems. Some of the obtained results improve and extend the recent existing results. Several examples are provided to show the main results obtained.

Citation: Qilin Wang, Liu He, Shengjie Li. Higher-order weak radial epiderivatives and non-convex set-valued optimization problems. Journal of Industrial & Management Optimization, 2019, 15 (2) : 465-480. doi: 10.3934/jimo.2018051
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