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
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。
Abstract: 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.
文章引用：杨志, 王仕伟, 冷震北, 匡艳. 变分不等式与不动点问题的非单调步长惯性投影算法[J]. 应用数学进展, 2025, 14(2): 228-243. https://doi.org/10.12677/aam.2025.142066

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