双层变分不等式的Levitin-Polyak适定性  

Levitin-Polyak Well-posedness of Variational Inequality with Variational Inequality Constraint

作　　者：彭明燕 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：《应用数学学报》2016年第3期362-372,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(10671135);教育部重点项目(212147)资助

摘　　要：本文首先引入了双层变分不等式的Levitin-Polyak适定性的定义,给出了相应适定性的度量性质.然后研究了双层变分不等式的Levitin-Polyak适定性与一般混合变分不等式的Levitin-Polyak适定性之间的关系.最后,在适当的条件下证明了双层变分不等式的适定性与其解的存在唯一性等价.In this paper, we first introduce the Levitin-Polyak well-posedness of variational inequality with variational inequality constraint. We also establish some metric characteri- zations of Levitin-Polyak well-posedness for variational inequality with variational inequality constraint. We give some relations between variational inequality with variational inequal- ity constraint and mixed variational inequality. Finally, we prove that the Levitin-Polyak well-posedness of variational inequality with variational inequality constraint is equivalent to the existence and uniqueness of solutions.

关 键 词：双层变分不等式 度量性质 Levitin-Polyak适定性 

分 类 号：O176.3[理学—数学] O178[理学—基础数学]