Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems

doi:10.1007/s40305-019-00275-8

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (2): 441-454.doi: 10.1007/s40305-019-00275-8

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Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems

Xin Xu, Yang-Dong Xu, Yue-Ming Sun

College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2018-07-09 Revised:2019-07-20 Online:2021-06-30 Published:2021-06-08
Contact: Yang-Dong Xu, Xin Xu, Yue-Ming Sun E-mail:xyd04010241@126.com;xuxin200888@126.com;S1402801830@163.com
Supported by:
This research was supported by the National Natural Science Foundation of China (No.11801051).

Abstract

Abstract: With the help of a level mapping, this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems. First, we introduce a kind of level mapping which generalizes one given in Han and Gong (Optimization 65:1337–1347, 2016). Then, we give a sufficient condition for the upper semicontinuity and the lower semicontinuity of the level mapping. Finally, in terms of the semicontinuity of the level mapping, we establish the upper semicontinuity and the lower semicontinuity of the minimal solution set mapping to parametric setvalued vector optimization problems under the C-Hausdorff continuity instead of the continuity in the sense of Berge.

Key words: Set-valued vector optimization problems, Level mapping, Solution set mapping, Upper semicontinuity, Lower semicontinuity

CLC Number:

Xin Xu, Yang-Dong Xu, Yue-Ming Sun. Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems[J]. Journal of the Operations Research Society of China, 2021, 9(2): 441-454.

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Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems

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