可数映射族的Tikhonov-Mann迭代的定量亚稳态

Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bot, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas-Rachfors and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov-Mann iteration.

映射族的Tikhonov-Mann迭代的渐近正则速率

Rates of asymptotic regularity of the Tikhonov-Mann iteration for families of mappings

该研究将希尔伯特空间中非扩张映射族的Krasnoselskii-Mann型强收敛迭代推广至W-双曲空间，算出其有效渐近正则速率，同时把Tikhonov-Mann迭代的相关结果从单映射拓展到映射族。

On modified Halpern and Tikhonov-Mann iterations

We show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Panyanak and the Tikhonov-Mann iteration introduced by H. Cheval and L. Leuştean as a generalization of an iteration due to Y. Yao et al. that has recently been studied by Boţ et al. can be reduced to each other in general geodesic settings. This, in particular, gives a new proof of the convergence result in Boţ et al. together with a generalization from Hilbert to CAT(0) spaces. Moreover, quantitative rates of asymptoti…

一般化随机Halpern方案的渐进行为

Asymptotic regularity of a generalised stochastic Halpern scheme

本文提出了一种广义随机Halpern迭代方案，提供了其渐进行为速率的统一分析，并探讨了其在强化学习中的应用。