非凸变分不等式的四步投影算法及其收敛性分析  

Convergence Analysis of Four-Step Projection Algorithm for Non-Convex Variational Inequalities

作　　者：张亮[1] 吴至友[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《西南大学学报（自然科学版）》2014年第10期109-113,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金(10971241);重庆市自然科学基金(cstc2013jjB00001;cstc2011jjA00010)

摘　　要：利用非凸变分不等式和不动点问题的等价关系,给出了一个新的求解非凸变分不等式的四步投影算法.该算法在现有的三步迭代算法基础上,利用校正方法建立了第四步迭代公式.最后在适当条件下证明了该算法的收敛性,所得结论推广了该领域内的一些最新结果.It is well known that the non-convex variational inequalities are equivalent to the fixed point problems .A new four-step projective algorithm is proposed for non-convex variational inequalities based on the equivalence .With the known three-step iterative algorithms as a special case and using the technique of updating ,a fourth-step iteration scheme is established .Finally ,the convergence criteria of the algorithms are proved under some mild conditions .The results in this paper can be viewed as an improvement and ex-tension of the previously known results for general variational inequalities .

关 键 词：非凸变分不等式 一致临近正则集 ξ 强单调算子 η-Lipschitz 连续算子 四步投影算法 

分 类 号：O177.91[理学—数学]