您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (7): 121-126.doi: 10.6040/j.issn.1671-9352.0.2021.657

•   • 上一篇    

向量混合变分不等式弱有效解集的非空有界性

杨秀凤(),范江华*()   

  1. 广西师范大学数学与统计学院, 广西 桂林 541006
  • 收稿日期:2021-10-05 出版日期:2023-07-20 发布日期:2023-07-05
  • 通讯作者: 范江华 E-mail:2055756246@qq.com;jhfan@gxnu.edu.cn
  • 作者简介:杨秀凤(1997—), 女, 硕士研究生, 研究方向为最优化理论. E-mail: 2055756246@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11801102)

Nonemptiness and boundedness of weakly efficient solution sets for vector mixed variational inequalities

Xiufeng YANG(),Jianghua FAN*()   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, China
  • Received:2021-10-05 Online:2023-07-20 Published:2023-07-05
  • Contact: Jianghua FAN E-mail:2055756246@qq.com;jhfan@gxnu.edu.cn

摘要:

利用标量混合变分不等式解集非空有界的充要条件, 以及凸函数序列的Mosco收敛性和对偶锥的连通性, 得到了自反Banach空间中向量混合变分不等式的弱有效解集为非空有界集的充要条件。

关键词: 向量混合变分不等式, 非空有界, C-F伪单调, Mosco收敛

Abstract:

By using the necessary and sufficient conditions for the nonemptiness and boundedness of the set of solutions for mixed scalar variational inequalities, the Mosco convergence of convex functions sequences and the connectedness of dual cones, the necessary and sufficient conditions for the weakly efficient solution sets of mixed vector variational inequalities in reflexive Banach spaces to be a nonempty bounded set are obtained.

Key words: vector mixed variational inequality, nonemptiness and boundedness, C-F pseudomonotone, Mosco convergence

中图分类号: 

  • O224.1
1 GIANNESSI F. Theorems of alternative, quadratic programs and complementarity problems[C]//Variational Inequalities and Complementarity Problems, New York: John Wiley and Sons, 1980: 151-186.
2 GOLESTANT M , SADEGHI H , TAVAN Y . Nonsmooth multiobjective problems and generalized vector variational inequalities using quasi-efficiency[J]. Journal of Optimization Theory and Applications, 2018, 179 (3): 896- 916.
doi: 10.1007/s10957-017-1179-z
3 HUANG Xuexiang , YANG Xiaoqi . Characterizations of nonemptiness and compactness of the set of weakly efficient solutions for convex vector optimization and applications[J]. Journal of Mathematical Analysis and Applications, 2001, 264 (2): 270- 287.
doi: 10.1006/jmaa.2001.7635
4 DENG Sien . Boundedness and nonemptiness of the efficient solution sets in multiobjective optimization[J]. Journal of Optimization Theory and Applications, 2010, 144 (1): 29- 42.
doi: 10.1007/s10957-009-9589-1
5 HU Rong , FANG Yaping . On the nonemptiness and compactness of the solution sets for vector variational inequalities[J]. Optimization, 2010, 59 (7): 1107- 1116.
doi: 10.1080/02331930903395600
6 HUANG Xuexiang , FANG Yaping , YANG Xiaoqi . Characterizing the nonemptiness and compactness of the solution set of a vector variational inequality by scalarization[J]. Journal of Optimization Theory and Applications, 2014, 162 (2): 548- 558.
doi: 10.1007/s10957-012-0224-1
7 FAN Jianghua , JING Yan , ZHONG Renyou . Nonemptiness and boundedness of solution sets for vector variational inequalities via topological method[J]. Journal of Global Optimization, 2015, 63 (1): 181- 193.
doi: 10.1007/s10898-015-0279-2
8 WANG Xing , HUANG Nanjing . Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces[J]. Journal of Industrial & Management Optimization, 2012, 9 (1): 57- 74.
9 ZHONG Renyou , HUANG Nanjing . Stability analysis for minty mixed variational inequality in reflexive Banach spaces[J]. Journal of Optimization Theory and Applications, 2010, 147 (3): 454- 472.
doi: 10.1007/s10957-010-9732-z
10 AUSLENDER A , TEBOULLE M . Asymptotic cones and functions in optimization and variational inequalities[M]. New York: Springer, 2003.
11 ADLY S , ERNST E . Well-positioned closed convex sets and well-positioned closed convex functions[J]. Journal of Global Optimization, 2004, 29 (4): 337- 351.
doi: 10.1023/B:JOGO.0000047907.66385.5d
12 ZHONG Renyou , HUANG Nanjing , CHO Y . Boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems with an application[J]. Journal of Inequalities and Applications, 2011, 2011 (1): 1- 15.
doi: 10.1186/1029-242X-2011-1
13 SALINETTI G , WETS J B . On the relations between two types of convergence for convex functions[J]. Journal of Mathematical Analysis and Applications, 1977, 60 (1): 211- 226.
doi: 10.1016/0022-247X(77)90060-9
No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报(理学版), 2013, 48(1): 1 -22 .
[2] 董伟伟. 一种具有独立子系统的决策单元DEA排序新方法[J]. J4, 2013, 48(1): 89 -92 .
[3] 张京友,张培爱,钟海萍. 进化图论在知识型企业组织结构设计中的应用[J]. J4, 2013, 48(1): 107 -110 .
[4] 罗斯特,卢丽倩,崔若飞,周伟伟,李增勇*. Monte-Carlo仿真酒精特征波长光子在皮肤中的传输规律及光纤探头设计[J]. J4, 2013, 48(1): 46 -50 .
[5] 田学刚, 王少英. 算子方程AXB=C的解[J]. J4, 2010, 45(6): 74 -80 .
[6] 霍玉洪,季全宝. 一类生物细胞系统钙离子振荡行为的同步研究[J]. J4, 2010, 45(6): 105 -110 .
[7] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[8] 杨永伟1,2,贺鹏飞2,李毅君2,3. BL-代数的严格滤子[J]. 山东大学学报(理学版), 2014, 49(03): 63 -67 .
[9] 李敏1,2,李歧强1. 不确定奇异时滞系统的观测器型滑模控制器[J]. 山东大学学报(理学版), 2014, 49(03): 37 -42 .
[10] 唐风琴1,白建明2. 一类带有广义负上限相依索赔额的风险过程大偏差[J]. J4, 2013, 48(1): 100 -106 .