Convergence of an Inertial Shadow Douglas-Rachford Splitting Algorithm for Monotone Inclusions

被引：10

作者：

Fan, Jingjing ^{[1
]}

Qin, Xiaolong ^{[2
]}

Tan, Bing ^{[1
]}

机构：

[1] Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, Chengdu, Peoples R China

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

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2021年 / 42卷 / 14期

关键词：

Inertial algorithm; Monotone inclusion; Shadow Douglas-Rachford splitting algorithm; Three-operator splitting; STEEPEST-DESCENT METHOD; FEASIBILITY PROBLEMS;

D O I：

10.1080/01630563.2021.2001749

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.

引用

页码：1627 / 1644

页数：18

共 50 条

[31] Douglas-Rachford splitting method for semidefinite programming
Dong Y.
Journal of Applied Mathematics and Computing, 2016, 51 (1-2) : 569 - 591
[32] Convergence of the preconditioned proximal point method and Douglas-Rachford splitting in the absence of monotonicity
Evens, Brecht
Pas, Pieter
Latafat, Puya
Patrinos, Panagiotis
MATHEMATICAL PROGRAMMING, 2025,
[33] Diagonal Scaling in Douglas-Rachford Splitting and ADMM
Giselsson, Pontus
Boyd, Stephen
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 5033 - 5039
[34] The Douglas-Rachford algorithm for a hyperplane and a doubleton
Bauschke, Heinz H.
Dao, Minh N.
Lindstrom, Scott B.
JOURNAL OF GLOBAL OPTIMIZATION, 2019, 74 (01) : 79 - 93
[35] ADAPTIVE DOUGLAS-RACHFORD SPLITTING ALGORITHM FROM A YOSIDA APPROXIMATION STANDPOINT
Liu, Zihan
Ramchandran, Kannan
SIAM JOURNAL ON OPTIMIZATION, 2021, 31 (03) : 1971 - 1998
[36] On the order of the operators in the Douglas-Rachford algorithm
Bauschke, Heinz H.
Moursi, Walaa M.
OPTIMIZATION LETTERS, 2016, 10 (03) : 447 - 455
[37] Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions
M. Marques Alves
Marina Geremia
Numerical Algorithms, 2019, 82 : 263 - 295
[38] The Douglas-Rachford Algorithm in the Absence of Convexity
Borwein, Jonathan M.
Sims, Brailey
FIXED-POINT ALGORITHMS FOR INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2011, 49 : 93 - 109
[39] A convergent relaxation of the Douglas-Rachford algorithm
Nguyen Hieu Thao
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2018, 70 (03) : 841 - 863
[40] Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng's F-B four-operator splitting method for solving monotone inclusions
Marques Alves, M.
Geremia, Marina
NUMERICAL ALGORITHMS, 2019, 82 (01) : 263 - 295

← 1 2 3 4 5 →