Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods

doi:10.1007/s40305-018-0230-6

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (1): 79-97.doi: 10.1007/s40305-018-0230-6

收稿日期:2017-09-15 修回日期:2018-06-30 出版日期:2021-03-11 发布日期:2021-03-11

Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods

Pei-Pei Liu, Hong-Zhi Wei, Chun-Rong Chen, Sheng-Jie Li

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2017-09-15 Revised:2018-06-30 Online:2021-03-11 Published:2021-03-11
Contact: Chun-Rong Chen, Pei-Pei Liu, Hong-Zhi Wei, Sheng-Jie Li E-mail:chencr1981@163.com;peipeiliu1992@163.com;hongzhiwei0922@163.com;lisj@cqu.edu.cn
Supported by:
This research was supported by the National Natural Science Foundation of China (Nos. 11301567 and 11571055) and the Fundamental Research Funds for the Central Universities (No. 106112017CDJZRPY0020).

摘要/Abstract

Abstract: The aim of this paper is to investigate the continuity of solution mappings for parametric set optimization problems with upper and lower set less order relations by scalarization methods. First, we recall some linear and nonlinear scalarization properties used to characterize the set order relations. Subsequently, we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods. Finally, we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems (both convex and nonconvex cases) under the monotonicity assumption and other suitable conditions. The results achieved do not impose the continuity of the set-valued objective mapping, which are obviously different from the related ones in the literature.

Key words: Upper semicontinuity, Lower semicontinuity, Parametric set optimization problems, Scalarization, Monotonicity

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2021, 9(1): 79-97.

Pei-Pei Liu, Hong-Zhi Wei, Chun-Rong Chen, Sheng-Jie Li. Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods[J]. Journal of the Operations Research Society of China, 2021, 9(1): 79-97.

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Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods

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