一类伪单调变分不等式与不动点问题的自适应惯性投影算法  

A Self-adaptive Inertial Projection Algorithm for a Classof Pseudomonotone Variational Inequalities and Fixed-Point Problems

作　　者：杨蓝翔 叶明露[1] YANG Lan-xiang;YE Ming-lu(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2023年第3期261-268,共8页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金面上项目(11871059);国家自然科学基金青年项目(11801455)。

摘　　要：在希尔伯特空间中提出了一种自适应惯性投影算法来求解伪单调变分不等式与不动点问题。通过加入自适应步长规则,新算法无需估计映射的Lipschitz系数。这优化了已有的算法,并在相同的假设条件下证明了算法所生成的序列从强收敛到变分不等式解集与不动点解集的交中一点。In this paper,a self-adaptive inertial projection algorithm is proposed for solving pseudomonotone variational inequalities and fixed-point problems in Hilbert space.The adding of a self-adaptive step size rule enables the new algorithm to do no estimation of Lipschitz modulus of the mapping.It is an optimization of the existing algorithm.Moreover,under the same assumption,it is proved that the sequence generated by the algorithm can strongly converge to a point in the intersection of the solution sets of variational inequalities and fixed points.

关 键 词：变分不等式 伪单调 不动点 自适应步长 惯性投影算法 

分 类 号：O224[理学—运筹学与控制论]