广义向量混合变分不等式的Levitin-Polyak适定性  

Levitin-Polyak Well-posedness of Generalized Vector Mixed Variational Inequalities

作　　者：朱莉[1] 夏福全[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2013年第5期655-662,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671135);教育部博士点基金(20105134120002);教育部重点项目(212147);四川省科技厅应用基础项目(2010JY0121)资助项目

摘　　要：首先给出了广义向量混合变分不等式的Levitin-Polyak-近似序列以及适定性的概念.然后,定义了广义向量混合变分不等式的gap函数,并证明了广义向量混合变分不等式的Levitin-Polyak-适定性与其相应的gap函数所定义的优化问题的Levitin-Polyak-适定性之间的等价关系.最后,研究了广义向量混合变分不等式的Levitin-Polyak-适定性的Furi-Vignoli型度量性质.In this paper, we first introduce the concepts of the Levitin-Polyak approximating sequences and the Levitin-Polyak wellposedness to the generalized vector mixed variational inequalities. We also define the gap function of the generalized vector mixed varia-tional inequalities and prove that the Levitin-Polyak well-posedness to the generalized vector mixed variational inequalities and the corresponding optimization problems are equivalent. After that, we investigate the Furi-Vignoll type metric characteristics of Levitin-Polyakwell-posedness to the generalized vector mixed variational inequalities,

关 键 词：Levitin—Polyak-适定性 广义向量混合变分不等式 标量函数 gap函数 优化问题 

分 类 号：O176.3[理学—数学] O178[理学—基础数学]