Iterative method with inertial terms for nonexpansive mappings: applications to compressed sensing

被引：54

作者：

Shehu, Yekini ^{[1
]}

Iyiola, Olaniyi S. ^{[2
]}

Ogbuisi, Ferdinard U. ^{[3
,4
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] Calif Univ Penn, Dept Math Comp Sci & Informat Syst, California, PA USA

[3] Univ Nigeria, Dept Math, Nsukka, Nigeria

[4] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa

来源：

NUMERICAL ALGORITHMS | 2020年 / 83卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Halpern-type algorithm; Inertial terms; Nonexpansive mappings; Strong convergence; Hilbert spaces; STRONG-CONVERGENCE THEOREMS; MAXIMAL MONOTONE-OPERATORS; FIXED-POINTS; THRESHOLDING ALGORITHM; ACCRETIVE-OPERATORS; GRADIENT METHODS; PROXIMAL METHOD; APPROXIMATION; SEQUENCES; KRASNOSELSKII;

D O I：

10.1007/s11075-019-00727-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our interest in this paper is to introduce a Halpern-type algorithm with both inertial terms and errors for approximating fixed point of a nonexpansive mapping. We obtain strong convergence of the sequence generated by our proposed method in real Hilbert spaces under some reasonable assumptions on the sequence of parameters. As applications, we present some strong convergence results for monotone inclusion, variational inequality problem, linear inverse problem, and LASSO problem in Compressed Sensing. Our result improves the rate of convergence of existing Halpern method for monotone inclusion, variational inequality problem, linear inverse problem and LASSO problem in compressed sensing as illustrated in our numerical examples both in finite and infinite dimensional Hilbert spaces.

引用

页码：1321 / 1347

页数：27

共 69 条

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