发表机构
Yunnan Normal University; Yunnan Key Laboratory of Modern Analytical Mathematics and Applications（云南师范大学; 现代分析数学及其应用云南省重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出自适应辛近端点算法（ASPPA），证明其平方范数项收敛率达O(1/k^2)，强单调情形下具指数收敛率，数值实验验证性能优异。
AI 中文摘要
近端点算法（PPA）是求解单调包含问题的基本方法。值得注意的是，若干关键凸优化算法已被证明是PPA的具体实例。鉴于PPA的重要性，人们对其加速变体的开发兴趣日益浓厚。然而，在某些特定情形下，PPA的收敛速度快于加速型PPA。本文主要研究一种自适应版本的辛加速PPA，称为自适应辛近端点算法（ASPPA）。我们首先证明，ASPPA关于平方范数项的收敛率为$O(1/k^2)$，这与某些加速PPA的收敛率相同。此外，我们表明，在求解强单调包含问题时，ASPPA具有指数收敛率。我们的数值实验表明，ASPPA的性能非常优异。
英文摘要
The proximal point algorithm (PPA) stands as a fundamental approach for solving monotone inclusion problems. Notably, several key convex optimization algorithms have been proven to be specific instances of PPA. Given the importance of the PPA, there has been growing interest in developing its accelerated variants. However, for some specific cases, the PPA converges faster than the accelerated PPAs. In this paper, we mainly study an adaptive version of symplectic accelerated PPA, called adaptive symplectic proximal point algorithm (ASPPA). We first prove that the convergence rate of ASPPA with respect to the square norm term is $O(1/k^2)$, which is the same as the convergence rate of some accelerated PPAs. Also, we show that ASPPA exists exponential convergence rate when solving strongly monotone inclusion problem. Our numerical experiments indicate that the performance of ASPPA is very good.
Comments23pages, 10 figures
