关于伪单调平衡问题和不动点问题的粘滞-次梯度方法  

On Viscosity-subgradient Methods for Pseudomonotone Equilibrium Problem and Fixed-point Problems

作　　者：闻道君[1] WEN Daojun(College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P. R. Chin)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数学进展》2017年第2期303-312,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金项目(No.11471059);重庆市前沿与应用基础研究项目(No.cstc2016jcyjA0101;No.cstc2014jcyjA00037);重庆市教委科技研究项目(No.KJ1500623;No.KJ1500634)

摘　　要：本文介绍了一个新的逼近伪单调平衡问题的解和广义渐近λ-严格伪压缩映象不动点的粘滞-次梯度方法,在Hilbert空间中建立了关于伪单调平衡问题和一簇广义渐近λ-严格伪压缩映象公共不动点的强收敛定理,并在收敛性分析中去掉了映象的一致Lipschitz连续性条件.In this paper, a new viscosity-subgradient method is introduced to approximate a common element of the set of solutions of a pseudomonotone equilibrium problem and the set of fixed points of a family of asymptotically strict pseudo-contractive mappings in the intermediate sense in a real Hilbert spacel Strong convergence theorems of the corresponding iterative sequences are obtained without the property of uniformly Lipschitz continuity defined on the underlying mappings in convergence analysis.

关 键 词：伪单调平衡问题 粘滞-次梯度方法 广义渐近λ-严格伪压缩映象 不动点 

分 类 号：O177.91[理学—数学]