扰动广义混合变分不等式的可解性

doi:10.16088/j.issn.1001-6600.2018.01.010

广西师范大学学报（自然科学版） ›› 2018, Vol. 36 ›› Issue (1): 76-83.doi: 10.16088/j.issn.1001-6600.2018.01.010

扰动广义混合变分不等式的可解性

唐国吉^1*,赵婷²,何登旭¹

1.广西民族大学理学院,广西南宁530006;
2.西南交通大学希望学院,四川成都610405

收稿日期:2017-05-30 出版日期:2018-01-20 发布日期:2018-07-17
通讯作者: 唐国吉(1979—),男,广西防城港人,广西民族大学副教授,博士。E-mail:guojvtang@126.com
基金资助:
国家自然科学基金(11561008);广西自然科学基金(2014GXNSFAA118006);广西高校优秀中青年骨干教师培养工程(桂教人[2014]39号);广西八桂学者专项(WBS-2014-04);广西民族大学相思湖青年学者(重点)创新团队(民大2015-13-02)

Solvability for Generalized Mixed Variational Inequalities with Perturbation

TANG Guoji^1*,ZHAO Ting²,HE Dengxu¹

1.School of Science,Guangxi University for Nationalities,Nanning Guangxi 530006,China;
2.Southwest Jiaotong University Hope College,Chengdu Sichuan 610405,China

Received:2017-05-30 Online:2018-01-20 Published:2018-07-17

摘要/Abstract

摘要： 本文主要研究扰动的广义混合变分不等式解的存在性问题。对集值映射引入2种扰动方式: 一种是通过连续的单值映射进行扰动;另一种是通过约束集的闸锥内部的向量进行扰动。在较弱的强制性条件下证明了扰动问题解的存在性。本文的结果在经济领域的某些价格均衡模型中有潜在的应用价值,推广和改善了一些新近文献的相应结果。

关键词: 混合变分不等式, 扰动, 存在性, 强制性条件

Abstract: The existence of solutions for a generalized mixed variational inequality with perturbation is investigated in this paper. Two perturbed ways of a set-valued mapping are introduced: one is perturbed by a continuous and single-valued mapping,and the other is perturbed by a vector in the interior of the barrier cone of the constrained set. Under rather weak conditions, it is shown that the generalized mixed variational inequality perturbed by two ways mentioned above has a solution. The main results may be used in some price equilibrium model in the field of economics, which generalize and improve some known results.

Key words: mixed variational inequality, perturbation, existence, coercivity condition

中图分类号:

O221.2

唐国吉,赵婷,何登旭. 扰动广义混合变分不等式的可解性[J]. 广西师范大学学报（自然科学版）, 2018, 36(1): 76-83.

TANG Guoji. Solvability for Generalized Mixed Variational Inequalities with Perturbation[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 76-83.

参考文献

[1] 张石生.变分不等式及其相关问题[M].重庆: 重庆出版社,2008.
[2] BIANCHI M,HADJISAVVAS N,SCHAIBLE S.Minimal coercivity conditions and exceptional families of elements in quasimonotone variational inequalities[J].Journal of Optimization Theory and Applications,2004,122(1):1-17. DOI:10.1023/B:JOTA.0000041728.12683.89.
[3] BIANCHI M,PINI R. Coercivity conditions for equilibrium problems[J]. Journal of Optimization Theory and Applications,2005,124(1): 79-92. DOI:10.1007/s10957-004-6466-9.
[4] DANIILIDIS A,HADJISAVVAS N. Coercivity conditions and variational inequalities[J]. Mathematical Programming,1999,86(2):433-438. DOI:10.1007/s101070050097.
[5] FACCHINEI F,PANG Jongshi.Finite-Dimensional variational inequalities and complementarity problems[M]. New York:Springer-Verlag,2003. DOI:10.1007/b97543.
[6] FAN Jianghua,WANG Xiaoguo.Solvability of generalized variational inequality problems for unbounded sets in reflexive Banach spaces[J].Journal of Optimization Theory and Applications,2009,143(1):59-74. DOI:10.1007/s10957-009-9556-x.
[7] HAN J,HUANG Z H,FANG S C.Solvability of variational inequality problems[J].Journal of Optimization Theory and Applications,2004,122(3):501-520. DOI:10.1023/B:JOTA.0000042593.74934.b7.
[8] HE Yiran.The Tikhonov regularization method for set-valued variational inequalities[J]. Abstract and Applied Analysis,2012,2012:172061.DOI:10.1155/2012/172061.
[9] 付冬梅,何诣然. 广义混合变分不等式的Tikhonov正则化方法[J].四川师范大学学报(自然科学版),2014,37(1): 12-17.DOI:10.3969/j.issn.1001-8395.2014.01.003.
[10] LI Fenglian,HE Yiran. Solvability of a perturbed variational inequality[J]. Pacific Journal of Optimization,2014,10(1): 105-111.
[11] 李择均,孙淑芹. 一个扰动变分不等式的可解性[J]. 数学物理学报,2016,36A(3): 473-480.
[12] 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.
[13] 殷洪友,徐成贤,张忠秀. F-互补问题及其与极小元问题的等价性[J]. 数学学报,2001,44(4): 679-686.
[14] TANG Guoji,HUANG Nanjing. Existence theorems of the variational-hemivariational inequalities[J]. Journal of Global Optimization,2013,56(2): 605-622. DOI:10.1007/s10898-012-9884-5.
[15] TANG Guoji,WANG Xing,WANG Zhongbao. Existence of variational quasi-hemivariational inequalities involving a set-valued operatorand a nonlinear term[J]. Optimization Letters,2015,9(1): 75-90. DOI:10.1007/s11590-014-0739-5.
[16] TANG Guoji,ZHOU Liwen,HUANG Nanjing. Existence results for a class of hemivariational inequality problems on Hadamard manifolds[J]. Optimization,2016,65(7): 1451-1461. DOI:10.1080/02331934.2016.1147036.
[17] AUBIN J P,FRANKOWSKA H. Set-valued analysis[M]. Basel: Birkhuser, 2008.
[18] KONNOV I V,VOLOTSKAYA E O. Mixed variational inequalities and economics equilibrium problems[J]. Journal of Applied Mathematics,2002,2(6): 289-314. DOI:10.1155/S1110757X02106012.
[19] KONNOV I V. Combined relaxation methods for variational inequalities[M]. Berlin: Springer-Verlag,2001.
[20] KONNOV I V. Mathematics in science and engineering volume 120: equilibrium models and variational inequalities[M]. Amsterdam: Elsevier,2007.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

扰动广义混合变分不等式的可解性

Solvability for Generalized Mixed Variational Inequalities with Perturbation

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

Metrics

本文评价

推荐阅读 0

[1]	项琴琴, 廖志贤, 李廷会, 蒋品群, 黄国现. 电网随机扰动下的光伏微网逆变器建模及控制研究[J]. 广西师范大学学报（自然科学版）, 2020, 38(1): 19-25.
[2]	朱娅萍, 屈国荣, 范江华. 不动点指数法研究拟变分不等式解的存在性[J]. 广西师范大学学报（自然科学版）, 2019, 37(4): 79-85.
[3]	王佳玉. 有限维空间中广义混合变分不等式的近似-似投影算法[J]. 广西师范大学学报（自然科学版）, 2019, 37(4): 86-93.
[4]	谢蓉,邹艳丽,傅杰. 基于动力学的电网发电机故障恢复策略研究[J]. 广西师范大学学报（自然科学版）, 2017, 35(1): 1-6.
[5]	戴静娱, 张学良, 邓敏艺, 谭惠丽. 位置扰动对激发介质中螺旋波动力学行为的影响[J]. 广西师范大学学报（自然科学版）, 2016, 34(2): 8-14.
[6]	章美月. 关于电子束聚焦系统模型的一些新结果[J]. 广西师范大学学报（自然科学版）, 2015, 33(1): 38-44.
[7]	涂登平, 刘晓冀. 矩阵乘积核心逆在0点特征投影的刻画[J]. 广西师范大学学报（自然科学版）, 2011, 29(1): 24-28.