非扩张映射和广义变分不等式迭代算法  

Iteration algorithms for nonexpansive mappings and generalized variational inequality

作　　者：高雷阜[1] 刘杰[1] 高鼎[1] 

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第5期704-707,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金青年基金资助项目(G010303);辽宁省教育厅基金资助项目(L2012103)

摘　　要：针对非扩张映射的不动点问题和Hilbert空间中广义变分不等式的问题,利用粘滞逼近算法,建立更一般的迭代过程,迭代算法在参数满足一定的条件下,得到非扩张映射的不动点集与Hilbert空间中广义变分不等式的公共元素,结果表明:该迭代序列所得到的结果满足某类变分不等式,强收敛性证明在较弱条件下论证了所建立的迭代算法的合理性和有效性.For nonexpansive mapping fixed point problems and Hilbert space generalized variational inequality problems, this paper constructed a more general iterative process by using of the viscous approximation algorithm. When the parameters satisfied with certain conditions, this iterative algorithm can be used to obtain non-expansion mapping fixed point set with Hilbert space generalized variational inequality common elements. The result of study shows that the result obtained from the iterative sequence satisfies certain variational inequalities. The strong convergence proved the rationality and effectiveness of the constructed iterative algorithm under the mild conditions.

关 键 词：Hillbert空间 粘滞逼近 非扩张映射 广义变分不等式 不动点 单调映射 集值映射 正规锥 

分 类 号：O221.2[理学—运筹学与控制论]