一种求解变分包含问题的Man迭代算法  

Mann-iterative algorithm for solving a class of variational inclusions

作　　者：李鹤[1] 

机构地区：[1]辽阳职业技术学院计算机科学系,辽宁辽阳111004

出　　处：《沈阳师范大学学报（自然科学版）》2011年第2期157-159,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(60673021)

摘　　要：首先回顾了与变分包含问题相关的一些基本概念。然后介绍H-单调算子的概念,接下来考虑一类带有H-单调算子的变分包含问题,该类变分包含问题可以涵盖前人研究过的几类变分问题和变分不等式问题,从而表明该类问题是已研究问题的有效推广深入研究。接下来笔者给出了预解算子的概念,并利用该概念进一步建立了变分包含问题与某个不动点问题的等价性。这种等价性允许使用预解算子技巧提出一种新型的Man迭代算法。最后对算法的收敛性进行了分析,在所给定理条件下,利用文献[3]中被广泛应用的一个引理,不仅可以证明这类变分包含问题存在唯一解,而且可以保证所提的新型Man迭代算法最终强收敛到原问题的唯一解。This paper firstly reviews some basic concepts corresponding to variational inclusions and then gives the definition of H-monotonic operator,and consider a class of variational inclusion problems involving H-monotone operators.This problem includes several classes of variational inequalities and variational inclusions as special cases,which shows that the problem is the generalization and further study of the existed problems.Next,the resolvent operator is defined,and by using this definition this paper establishs the equivalence between the variational inclusion problems and the fixed point problems.This equivalence allows us to suggest a new Mann type iterative algorithm for solving variational inclusions by using the resolvent operator technique.In the final part of this paper,this paper also discusses the convergence of the proposed algorithm.Under suitable conditions,this paper not only proves the existence and uniqueness of the solution by using the Lemma in [3],but also shows the strong convergence of the proposed algorithm.

关 键 词：变分包含 H-单调算子 预解算子技巧 迭代算法 不动点 

分 类 号：O177.1[理学—数学]