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

Qilin Wang; Liu He; Shengjie Li

doi:10.3934/jimo.2018051

Article Contents

2019, Volume 15, Issue 2: 465-480. Doi: 10.3934/jimo.2018051

This issue Previous Article Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming Next Article Asymptotics for a bidimensional risk model with two geometric Lévy price processes

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.
¹ Corresponding author.

Received: June 30, 2017

Revised: November 30, 2017

Early access: April 2018

Published: January 2019

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).

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Abstract

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.

Keywords:

Set-valued optimization problems,
higher-order weak radial epiderivatives,
optimality conditions,
weak efficient solutions,
Pareto efficient solutions.

Mathematics Subject Classification: 90C26, 90C46.

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