广义混合变分不等式的Tikhonov正则化方法  

The Tikhonov Regularization Method for Generalized Mixed Variational Inequalities

作　　者：付冬梅[1] 何诣然[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）》2014年第1期12-17,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11271274)资助项目

摘　　要：极小化问题可以转化为变分不等式,因此,变分不等式是解决极小化问题的一类重要方法.当变分不等式模型中的集合无界时,许多学者研究了各种各样的强制条件,以保证变分不等式的解存在.比较了几种主要强制性条件之间的关系,并在映射具有变分不等式性质时,给出了广义变分不等式解存在的证明,并且用Tikhonov正则化方法解决了不适定广义变分不等式解的存在性问题.广义混合变分不等式是比广义变分不等式更一般的模型,将广义变分不等式的Tikhonov正则化方法推广到广义混合变分不等式,以使Tikhonov正则化方法具有更加广泛的应用范围.为此,主要建立广义混合变分不等式的Tikhonov正则化理论.首先,在更弱的强制条件下,证明了广义混合变分不等式解的存在性,然后给出了广义混合变分不等式的Tikhonov正则化结果.A minimization problem can be transformed into a variational inequality, and this is a class of important methods for the solution of minimization problems. When the set in the variational inequality is unbounded, there are many coercivity conditions for the existence of solutions. Some scholars have compared the relationship among several main coercivity conditions, and proved that the ex- istence of solutions to the generalized variational inequality under the assumption of the mapping involved has variational inequality property. They also have solved the existence of solutions to the ill-posed generalized variational inequalities by the Tikhonov regulariza- tion method. As a generalization of the generalized variational inequality, the generalized mixed variational inequality is studied in this paper. We attempt to get some similar results for the generalized variational inequality, i. e. , to establish the Tikhonov regularization theory for generalized mixed variational inequality. Firstly, we prove the existence of solution of generalized mixed variational inequality under a rather weak coercivity condition. Then we give the Tikhonov regularization result for generalized mixed variational inequality.

关 键 词：广义混合变分不等式 解的存在性 TIKHONOV正则化 

分 类 号：O176[理学—数学] O178[理学—基础数学]