自反巴拿赫空间中广义变分不等式的稳定性与Tikhonov正则化(英文)  

Stability and Tikhonov regularization for generalized variational inequality in reflexive Banach spaces

作　　者：罗雪萍[1] 周武[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2015年第2期210-213,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：The National Natural Science Foundation of China(61379019);the Fundamental Research Funds for the Central Universities,Southwest University for Nationalities(2014NZYQN29)

摘　　要：在自反巴拿赫空间中,介绍了广义变分不等式的Tikhonov正则化及其相关理论.首先讨论了映射被扰动变分不等式的稳定性结果.基于稳定性,给出了Tikhonov正则化的变分不等式解集的某些特征.此结果推广了该领域已有的研究结果.Tikhonov regularization for generalized variational inequalities is introduced and the corresponding theory is established in reflexive Banach spaces. For this purpose, firstly the stability results of variational inequalities with the mapping perturbed are discussed in reflexive Banach spaces. Moreover, based on the above stability results, some characterizations for the solution sets of Tikhonov regularized variational inequalities are given in reflexive Banach spaces. The results presented in this paper generalize some known results in this area.

关 键 词：TIKHONOV正则化 稳定性 广义变分不等式 强制条件 

分 类 号：O177.2[理学—数学]