Continuity of solutions mappings of parametric set optimization problems

Jiawei Chen; Guangmin Wang; Xiaoqing Ou; Wenyan Zhang

doi:10.3934/jimo.2018138

Article Contents

2020, Volume 16, Issue 1: 25-36. Doi: 10.3934/jimo.2018138

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Continuity of solutions mappings of parametric set optimization problems

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2.
School of Economics and Management, China University of Geosciences, Wuhan 430074, China
3.
College of Management, Chongqing College of Humanities, Science & Technology, Chongqing 401524, China
4.
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

* Corresponding author: Jiawei Chen
* Corresponding author: Jiawei Chen

Received: December 2016

Revised: November 2017

Early access: September 2018

Published: October 2019

This research is supported by the Natural Science Foundation of China (Nos: 11571055, 11401487, 71471167), the Basic and Advanced Research Project of Chongqing (cstc2016jcyjA0239, cstc2015jcyjBX0131), the China Postdoctoral Science Foundation (No: 2015M582512) and the Fundamental Research Funds for the Central Universities.

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Abstract

Set optimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on the continuity of the strict (weak) minimal solution set mapping of parametric set-valued vector optimization problems with the lower set less order relation. We firstly introduce a concept of strict lower level mapping of parametric set-valued vector optimization problems. Moreover, the upper and lower semicontinuity of the strict lower level mapping are obtained under some suitable conditions. Lastly, the sufficient condition for the continuity of the strict minimal solution set mappings of parametric set optimization problems are established by a new proof method, which is different from that in [27,28].

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Mathematics Subject Classification: Primary: 49J53; Secondary: 49K40, 90C30.

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Figure 1. The strict $K$-quasiconvexity of $F(\cdot,\lambda)$ with $\lambda = 0.1$

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