变分不等式与不动点问题的非单调步长惯性投影算法  

Projection Algorithms with Line Search Process for Variational Inequality and Fixed Point Problems

作　　者：杨志 王仕伟 冷震北 匡艳 

机构地区：[1]重庆对外经贸学院数学与计算机学院,重庆

出　　处：《应用数学进展》2025年第2期228-243,共16页Advances in Applied Mathematics

基　　金：资助项目1:KYZK2024027:变分不等式与不动点问题非单调步长的惯性投影算法。资助项目2:KYZK2024010:图像处理中的张量离散不适定问题及其高性能迭代算法研究。资助项目3:KYZK2024003:变分不等式与不动点问题在NASH群体博弈的应用研究。

摘　　要：文章针对实Hilbert空间中的单调变分不等式和不动点连续映射的凸可行性问题,提出了一种非单调步长算法来求解。该算法利用可行集的信息构造特殊半空间,以及结合外梯度方法构造半空间。每次向两个半空间作投影。同时结合惯性加速技巧与Mann迭代方法,在一定条件下,建立了所提算法的弱收敛性定理。最后,我们进行了一些计算测试,以证明所提算法的效率和优点,并与现有算法进行了比较。This paper presents a new inertial subgradient extragradient algorithm designed to solve variational inequalities and fixed point problems in real Hilbert spaces. Integrating the Mann iteration method with the subgradient extragradient approach and employing inertial acceleration techniques, the algorithm constructs a half-space using subgradient information and projects onto it. Step lengths are determined via a line search procedure, eliminating the need to compute the Lipschitz constant of the mapping. The algorithm’s weak convergence is established under assumptions like the pseudo-nonexpansiveness of the mappings. Finally, Numerical experiments additionally illustrate the algorithm’s advantages over existing approaches in the literature.

关 键 词：次梯度外梯度算法 类Mann选代方法 弱收敛 变分不等式 不动点问题 

分 类 号：O17[理学—数学]