Connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets in complete metric space

被引：4

作者：

Shao, Chong-Yang ^{[1
]}

Peng, Zai-Yun ^{[1
]}

Xiao, Yi-Bin ^{[2
]}

Zhao, Yong ^{[1
]}

机构：

[1] Chongqing JiaoTong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610000, Peoples R China

来源：

OPTIMIZATION LETTERS | 2022年 / 16卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Generalized vector equilibrium problems; Solution sets; Scalarization function; Connectedness; Free-disposal set;

D O I：

10.1007/s11590-021-01725-0

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, the connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets (GVEPVF) in complete metric space is discussed. Firstly, by virtue of Gerstewitz scalarization functions and oriented distance functions, a new scalarization function omega is constructed and some properties of it are given. Secondly, with the help of omega, the existence of solutions for scalarization problems (GVEPVF)(omega) and the relationship between the solution sets of (GVEPVF)(omega) and (GVEPVF) are obtained. Then, under some suitable assumptions, sufficient conditions of (path) connectedness of solution sets for (GVEPVF) are established. Finally, as an application, the connectedness results of E-efficient solution set for a class of vector programming problems are derived. The obtained results are new, and some examples are given to illustrate the main results.

引用

页码：2073 / 2093

页数：21

共 42 条

[1] Connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets in complete metric space
Chong-Yang Shao
Zai-Yun Peng
Yi-Bin Xiao
Yong Zhao
Optimization Letters, 2022, 16 : 2073 - 2093
[2] Connectedness of the solution sets for generalized vector equilibrium problems
Cui, Chong
Li, Shengjie
PACIFIC JOURNAL OF OPTIMIZATION, 2023, 19 (03): : 423 - 440
[3] Continuity of the solution set mappings to parametric unified weak vector equilibrium problems via free-disposal sets
Zhou, Daqiong
Peng, Zaiyun
Lin, Zhi
Wang, Jingjing
RAIRO-OPERATIONS RESEARCH, 2024, 58 (06) : 5301 - 5308
[4] Arcwise Connectedness of the Solution Sets for Generalized Vector Equilibrium Problems
Li, Qiuying
Wang, Sanhua
MATHEMATICS, 2021, 9 (20)
[5] Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems
X. H. Gong
Journal of Optimization Theory and Applications, 2007, 133 : 151 - 161
[6] Connectedness of the solution sets and scalarization for vector equilibrium problems
Gong, X. H.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 133 (02) : 151 - 161
[7] ON THE STABILITY OF SOLUTIONS FOR THE GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS VIA FREE-DISPOSAL SET
Wang, Jingjing
Peng, Zaiyun
Lin, Zhi
Zhou, Daqiong
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2021, 17 (02) : 869 - 887
[8] Connectedness of Solution Sets of Strong Vector Equilibrium Problems with an Application
Xu, Yangdong
Zhang, Pingping
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 178 (01) : 131 - 152
[9] Connectedness of Solution Sets of Strong Vector Equilibrium Problems with an Application
Yangdong Xu
Pingping Zhang
Journal of Optimization Theory and Applications, 2018, 178 : 131 - 152
[10] CONNECTEDNESS AND PATH-CONNECTEDNESS OF SOLUTION SETS TO SYMMETRIC VECTOR EQUILIBRIUM PROBLEMS
Zhong, Ren-you
Huang, Nan-jing
Wong, Mu-Ming
TAIWANESE JOURNAL OF MATHEMATICS, 2009, 13 (2B): : 821 - 836

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