Inertial Krasnoselskii-Mann Iterations

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-03-26 DOI:10.1007/s11228-024-00713-7

Juan José Maulén, Ignacio Fierro, Juan Peypouquet

引用次数: 0

Abstract

We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.

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惯性 Krasnoselskii-Mann 迭代

我们确定了惯性 Krasnoselskii-Mann 迭代对准无穷算子族共同定点的弱收敛性，以及残差消失的非渐近速率估计值。在准契约背景下，我们获得了强收敛性和线性收敛性。在这两种情况下，我们都强调了与非惯性情况的关系，并证明从一种制度到另一种制度是一个连续的过程。我们还提供了惯性初等二元法和惯性三运算器分割算法的数值示例，这两种算法的性能均优于非惯性算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.