一种新的求解拟单调变分不等式的惯性投影算法
A New Inertial Projection Algorithm for Solving Quasimonotone Variational Inequalities
摘要: 2023年，叶和邓[运筹学学报，2023，27(01)：127-137]提出了一种新的求解拟单调变分不等式的压缩投影算法(简称NPCA)。NPCA结合了向前向后分裂算法(简称FBSA)和压缩投影算法(简称PCA)来减少算法的迭代步数。在此基础上，本文提出了惯性的NPCA算法，简称为INPCA，并在与NPCA相同的假设条件下，证明了INPCA的全局收敛性。数值实验结果表明惯性方法能进一步加速NPCA。
Abstract: In 2023, Ye and Deng [Operations Research Transactions, 2023, 27(01): 127-137] introduced a new projection and contraction algorithm (NPCA) for solving quasimonotone variational inequalities. NPCA combines the forward backward splitting algorithm (FBSA) and the projection and contraction algorithm (PCA) to reduce iterations numbers. By incorporating an inertial step, we extend it to the inertial NPCA (INPCA). The global convergence is proven under the original assumptions, and numerical experiments confirm that the inertial step accelerates convergence.
文章引用：魏京晶, 叶明露. 一种新的求解拟单调变分不等式的惯性投影算法[J]. 应用数学进展, 2026, 15(2): 165-177. https://doi.org/10.12677/aam.2026.152058

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