Tikhonov-Mann迭代的渐近正则性的二次率

Optimization Methods and Software Pub Date : 2021-07-15 DOI:10.1080/10556788.2022.2060974

Horaţiu Cheval, Laurentiu Leustean

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引用次数: 8

摘要

本文计算了w -双曲空间中Tikhonov-Mann迭代的渐近正则性的二次率。该迭代是bolui, Csetnek和Meier最近在Hilbert空间中定义的修正Mann迭代的非线性设置的扩展。进一步，我们证明了具有Tikhonov正则化项的Douglas-Rachford和forward-backward算法是Hilbert空间中Tikhonov - mann迭代的特殊情况。

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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 Boţ, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas–Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov–Mann iteration.

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Optimization Methods and Software

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