论文标题
确切的最佳加速复杂性，用于定点迭代
Exact Optimal Accelerated Complexity for Fixed-Point Iterations
论文作者
论文摘要
尽管在整个应用数学过程中广泛使用了定点迭代，但尚未建立非专业非线性运算符的一般固定点问题的最佳收敛率。这项工作提出了一种加速机制，可与非专业操作员，承包商运营商以及满足Hölder-type增长条件的非专业操作员进行定义迭代。然后，我们提供匹配的复杂性下限，以建立非专业和承包设置中加速机制的确切最佳性。最后，我们提供了CT成像，最佳运输和分散优化的实验，以证明加速机制的实际有效性。
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration mechanism for fixed-point iterations with nonexpansive operators, contractive operators, and nonexpansive operators satisfying a Hölder-type growth condition. We then provide matching complexity lower bounds to establish the exact optimality of the acceleration mechanisms in the nonexpansive and contractive setups. Finally, we provide experiments with CT imaging, optimal transport, and decentralized optimization to demonstrate the practical effectiveness of the acceleration mechanism.
