广义混合变分不等式的weak-sharp解及算法的有限收敛  

Weak-sharp Solutions for Generalized Mixed Variational Inequalities and Finite Termination of Iterative Algorithms

作　　者：余静 夏福全 YU Jing;XIA Fuquan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2020年第5期590-596,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：教育部科学技术重点项目(212147)。

摘　　要：提出广义混合变分不等式问题的解集满足的weak-sharp条件,并通过约束集的支撑函数的一些性质,获得weak-sharp条件的等价刻画.在广义混合变分不等式问题的解集满足weak-sharp条件之下,还获得任意迭代算法有限收敛的等价条件,其中有限收敛指算法在有限次迭代后,得到广义混合变分不等式问题的精确解.最后,以广义混合变分不等式问题的超投影近似点算法为特例,在一定的条件下,获得该算法的有限收敛性.In this paper,we introduce the weak-sharp condition satisfying the solution set of the generalized mixed variational inequality problem. We propose the equivalent characterizations of weak-sharp condition by some properties of the support function of the constraint set. In addition,under the solution set of generalized mixed variational inequalities satisfied weak-sharp condition,we obtain equivalent conditions of the arbitrary finite convergent iterative algorithm. After finite iterations,the exact solution of generalized mixed variational inequalities is got by finite convergent iterative algorithm. Finally,we take a special example of the hybrid projection-proximal point algorithm for generalized mixed variational inequalities,obtaining the finite convergence of the algorithm under certain conditions.

关 键 词：广义混合变分不等式 weak-sharp条件 有限收敛 超投影近似点算法 

分 类 号：O176[理学—数学] O178[理学—基础数学]