[1]陈斌,王浩智.集值向量均衡问题近似解映射的连续性[J].华侨大学学报(自然科学版),2020,41(2):272-276.[doi:10.11830/ISSN.1000-5013.201909018]
 CHEN Bin,WANG Haozhi.Continuity of Approximate Solution Maps of Set-Valued Vector Euqilibrium Problems[J].Journal of Huaqiao University(Natural Science),2020,41(2):272-276.[doi:10.11830/ISSN.1000-5013.201909018]
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集值向量均衡问题近似解映射的连续性()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第41卷
期数:
2020年第2期
页码:
272-276
栏目:
出版日期:
2020-03-20

文章信息/Info

Title:
Continuity of Approximate Solution Maps of Set-Valued Vector Euqilibrium Problems
文章编号:
1000-5013(2020)02-0272-05
作者:
陈斌 王浩智
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
CHEN Bin WANG Haozhi
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
向量均衡问题 近似解映射 Hausdorff连续性 向量优化问题
Keywords:
vector equilibrium problems approximate solution maps Hausdorff continuity vector optimization problems
分类号:
O183.1
DOI:
10.11830/ISSN.1000-5013.201909018
文献标志码:
A
摘要:
研究局部凸Hausdorff拓扑向量空间中扰动下的集值向量均衡问题的原问题和对偶问题.建立原问题和对偶问题近似解映射的Hausdorff上半连续性和Hausdorff下半连续性的充分条件,改进和推广Anh等的研究结果.
Abstract:
This paper studies the primal problem and dual problem of set-valued vector equilibrium under perturbation in locally convex Hausdorff topological vector spaces. Sufficient conditions for the Hausdorff upper semi-continuity and Hausdorff lower semi-continuity of the approximate solution maps. Our result improves and generalizes the existing results of Anh et al.

参考文献/References:

[1] BLUM E,OETTLI W.From optimization and variational inequalities to equilibrium problems[J].Math Stud,1994,63(1/2/3/4):123-145.DOI:10.1093/jpids/pix105/4823046.
[2] BIANCHI M,SCHAIBLE S.Generalized monotone bifunctions and equilibrium problems[J].J Optim Theory Appl,1996,90:31-43.DOI:10.1007/BF02192244.
[3] BIANCHI M,HADJISAVVAS N,SCHAIBLE S.Equilibrium problems with generalized monotone bifunctions[J].J Optim Theory Appl,1997,92:527-542.DOI:10.1023/A:1022603406244.
[4] GONG Xunhua.Strong vector equilibrium problems[J].J Glob Optim,2006,36(3):339-349.DOI:10.1007/s10898-006-9012-5.
[5] HAN Yu,HUANG Nanjing.Existence and stability of solutions for a class of generalized vector equilibrium problems[J].Positivity,2016,20(4):829-846.DOI:10.1007/s11117-015-0389-6.
[6] HAN Yu,HUANG Nanjing.Some characterizations of the approximate solutions to generalized vector equilibrium problems[J].J Ind Manag Optim,2016,12(3):1135-1151.DOI:10.3934/jimo.2016.12.1135.
[7] HAI N X,KHANH P Q,QUAN N H.On the existence of solutions to quasivariational inclusion problems[J].J Glob Optim,2009,45(4):565-581.DOI:10.1007/s10898-008-9390-y.
[8] KHANHP Q,LONG V S T.Invariant-point theorems and existence of solutions to optimization-related problems[J].J Glob Optim,2014,58(3):545-564.DOI:10.1007/s10898-013-0065-y.
[9] KIM W K,KUM S,LEE K H.Semicontinuity of the solution multifunctions of the parametric generalized operator equilibrium problems[J].Nonlinear Anal,2009,71(12):e2182-e2187.DOI:10.1016/j.na.2009.04.036.
[10] LI X B,LI Shihong.Continuity of approximate solution mapping for parametric equilibrium problems[J].J Glob Optim,2011,51(3):541-548.DOI:10.1007/s10898-010-9641-6.
[11] LI S J,LIU M H,ZHANG Y,et al.Continuity of solution mappings to parametric generalized strong vector equilibrium problems[J].J Glob Optim,2013,55(3):597-610.DOI:10.1007/s10898-012-9985-1.
[12] CHEN Bin,HUANG Nanjing.Continuity of solution mapping to parametric generalized vector equilibrium problems[J].J Glob Optim,2013,56(4):1515-1528.DOI:10.1007/s10898-012-9904-5.
[13] HAN Yu,HUANG Nanjing,YAO J C.Connectedness and stability of the approximate solutions togeneralized vector quasi-equilibrium problems[J].J Nonlinear Convex A,2016,18(6):1079-1101.
[14] ANH L Q,KHANH P Q,TAM T N.On Hölder continuity of approximate solutions to parametric equilibrium problems[J].Nonlinear Anal,2012,75(4):2293-2303.DOI:10.1016/j.na.2011.10.029.
[15] LI S J,CHEN C R,LI X B,et al.Hölder continuity and upper estimates of solutions to vector quasi-equilibrium problems[J].Eur J Oper Res,2011,210(2):148-157.DOI:10.1016/j.ejor.2010.10.005.
[16] ANH L Q,KHANH P Q,TAM T N.Continuity of approximate solution maps of primal and dualvector equilibrium problems[J].Optim Lett,2019,13(2):201-211.DOI:10.3934/jimo.2017013.
[17] AUBIN J P,EKELAND I.Applied nonlinear analysis[M].New York:Wiley,1984.
[18] AUBIN J P,FRANKOWSKA H.Set-valued analysis[M].Boston:Birkhäuser,1990.
[19] MIN Chao,FAN Feifei,YANG Zhaozhong,et al.An iterative algorithm for the nonlinear MC2 model with variational inequality method[J].Mathematics,2019,7(6):514-526.DOI:10.3390/math7060514.

备注/Memo

备注/Memo:
收稿日期: 2019-09-17
通信作者: 陈斌(1984-),男,讲师,博士,主要从事变分不等式、向量优化和均衡问题的研究.E-mail:270267387@qq.com.
基金项目: 福建省高校创新团队发展计划(2018年度); 福建省泉州市高层次人才团队资助项目(2017ZT012); 华侨大学高层次人才科研启动项目(605-50Y14040)
更新日期/Last Update: 2020-03-20