论文标题
快速krasnosel'skii-mann算法，其固定点迭代的收敛速率$ o \ left（\ frac {1} {k} {k} {k} \ right）$
Fast Krasnosel'skii-Mann algorithm with a convergence rate of the fixed point iteration of $o\left(\frac{1}{k}\right)$
论文作者
论文摘要
Krasnosel'skii-Mann（KM）算法是最基本的迭代方案，旨在在真正的Hilbert空间的框架中找到平均操作员的固定点，因为它位于各种数值算法的核心，用于求解单调综合和CONVEX OPTINVES优化问题。我们通过Nesterov的动量更新增强了Krasnosel'skii-Mann算法，并表明所得的数值方法表现出$ O（1/K）$的固定点残留率的收敛速率，同时保留了迭代的弱收敛到操作员固定点的弱收敛性。数值实验说明了所得的所谓快速算法在各种固定点迭代方案上以及其振荡行为的优越性，这是Nesterov的动量优化算法的特定特定的。
The Krasnosel'skii-Mann (KM) algorithm is the most fundamental iterative scheme designed to find a fixed point of an averaged operator in the framework of a real Hilbert space, since it lies at the heart of various numerical algorithms for solving monotone inclusions and convex optimization problems. We enhance the Krasnosel'skii-Mann algorithm with Nesterov's momentum updates and show that the resulting numerical method exhibits a convergence rate for the fixed point residual of $o(1/k)$ while preserving the weak convergence of the iterates to a fixed point of the operator. Numerical experiments illustrate the superiority of the resulting so-called Fast KM algorithm over various fixed point iterative schemes, and also its oscillatory behavior, which is a specific of Nesterov's momentum optimization algorithms.
