广义混合变分不等式的Levitin-Polyak适定性  

Levitin-Polyak Well-posedness of Generalized 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,成都610066

出　　处：《数学物理学报（A辑）》2012年第4期633-643,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10671135);四川省科技厅应用基础项目(2010JY0121)资助

摘　　要：首先给出广义混合变分不等式的Levitin-Polyak-α-近似序列以及适定性的定义.然后,定义广义混合变分不等式的gap函数并证明广义混合变分不等式的Levitin-Polyak适定性与其相应的gap函数的极小化问题的Levitin-Polyak适定性之间的等价性.最后,研究广义混合变分不等式的(广义)Levitin-Polyak-α-适定性的Furi-Vignoli型度量性质.In this paper,we introduce the concepts of the Levitin-Polyak-a-approximating sequences and the Levitin-Polyak-a-well-posedness to the generalized mixed variational inequalities.We also define the gap function of the generalized mixed variational inequalities and prove that the Levitin-Polyak well-posedness to the generalized mixed variational inequalities and the corresponding minimization problems are equivalent.After that,we investigate the Puri-Vignoli type metric characteristics of （generalized） Levitin-Polyak well-posedness to the generalized mixed variational inequalities.

关 键 词：Levitin-Polyak-α-适定性 广义混合变分不等式 gap函数 极小化问题 

分 类 号：O176.3[理学—数学] O178[理学—基础数学]