论文标题
两步惯性近端算法的收敛结果
Convergence Results of Two-Step Inertial Proximal Point Algorithm
论文作者
论文摘要
本文提出了一种两点惯性近端算法，以在希尔伯特空间中找到最大单调算子的零。我们获得了较弱的收敛结果，并从非共性算法中获得了我们所提出的算法的非反应$ O（1/N）$收敛率。我们的结果应用于各种众所周知的凸优化方法，例如乘数的近端方法和交替的乘数方法。给出数值结果以证明我们方法对文献中其他相关方法的加速行为。
This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature.
