New strong convergence method for the sum of two maximal monotone operators
type: Item
instance of: scholarly article
title: New strong convergence method for the sum of two maximal monotone operators
author: Y. Shehu
author: Qiao-Li Dong
author: Lulu Liu
author: Jen-Chih Yao
published in: Optimization and Engineering
publication date: 2022-01-20T00:00:00Z
review text: A significant inclusion problem based on the sum of two set-valued maximal operators in Hilbert spaces is examined. Under proper hypotheses, the authors develop some of the corresponding point algorithms, with original contributions on the strong convergence of the inertial Douglas-Rachford splitting method, completed by adequated numerical examples and references.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 7460650
zbMATH Keywords: set-valued maximal monotone operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: point algorithm
zbMATH Keywords: strong convergence
zbMATH Keywords: inertial Douglas-Rachford splitting method
reviewed by: Vasile Postolică
describes a project that uses: SPGL1
describes a project that uses: L1TestPack
MaRDI profile type: Publication
full work available at URL: s11081-020-09544-5
OpenAlex ID: W3046619570
cites work: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
cites work: Convergence of a relaxed inertial forward-backward algorithm for structured monotone inclusions
cites work: A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
cites work: Convex analysis and monotone operator theory in Hilbert spaces
cites work: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
cites work: The viscosity approximation forward-backward splitting method for zeros of the sum of monotone operators
cites work: An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems
cites work: Inertial Douglas-Rachford splitting for monotone inclusion problems
cites work: Iterative methods for fixed point problems in Hilbert spaces
cites work: A generalized forward-backward splitting method for solving a system of quasi variational inclusions in Banach spaces
cites work: A generalized forward-backward splitting method for solving quasi inclusion problems in Banach spaces
cites work: An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces
cites work: Solving monotone inclusions via compositions of nonexpansive averaged operators
cites work: A strong convergence result involving an inertial forward-backward algorithm for monotone inclusions
cites work: Inertial projection and contraction algorithms for variational inequalities
cites work: On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
cites work: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
cites work: The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
cites work: A dual algorithm for the solution of nonlinear variational problems via finite element approximation
cites work: Tseng type methods for solving inclusion problems and its applications
cites work: Q3995612
cites work: Q4144736
cites work: On the Convergence of the Proximal Point Algorithm for Convex Minimization
cites work: On the convergence rate of Douglas-Rachford operator splitting method
cites work: Iterative selection methods for common fixed point problems
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators
cites work: Forward-backward splitting methods for accretive operators in Banach spaces
cites work: Constructing Test Instances for Basis Pursuit Denoising
cites work: An inertial forward-backward algorithm for monotone inclusions
cites work: Operator Splitting
cites work: Convergence theorems for inertial KM-type algorithms
cites work: Q5618030
cites work: Proximité et dualité dans un espace hilbertien
cites work: Weak and strong convergences of the generalized penalty Forward–Forward and Forward–Backward splitting algorithms for solving bilevel hierarchical pseudomonotone equilibrium problems
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: Iterative approximations for zeros of sum of accretive operators in Banach spaces
cites work: Convergence Rate Analysis of Inertial Krasnoselskii–Mann Type Iteration with Applications
cites work: Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces
cites work: Strong convergence result of forward-backward splitting methods for accretive operators in Banach spaces with applications
cites work: An efficient projection-type method for monotone variational inequalities in Hilbert spaces
cites work: Forcing strong convergence of proximal point iterations in a Hilbert space
cites work: On Weak Convergence of the Douglas–Rachford Method
cites work: Strong convergence of a forward-backward splitting method with a new step size for solving monotone inclusions
cites work: Inertial methods for fixed point problems and zero point problems of the sum of two monotone mappings
cites work: Accelerated and inexact forward-backward algorithms
cites work: Strong convergence of the forward–backward splitting method with multiple parameters in Hilbert spaces
cites work: Projective splitting methods for sums of maximal monotone operators with applications
DOI: 10.1007/S11081-020-09544-5
Recommended article: Strong convergence of a splitting projection method for the sum of maximal monotone operators
Recommended article: Strong convergence of monotone hybrid method for maximal monotone operators and hemirelatively nonexpansive mappings
Recommended article: Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
Recommended article: Q4981939
Recommended article: On the sum of two maximal monotone operators
Recommended article: Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces
Recommended article: Strong convergence of a splitting proximal projection method for the sum of two maximal monotone operators
Recommended article: On an iterative method for finding a zero to the sum of two maximal monotone operators

New strong convergence method for the sum of two maximal monotone operators (Recommended article)
Recommended article: On the regularization of the sum of two maximal monotone operators
Similarity Score: 0.904288
Recommender Run: Recommender Run 3

New strong convergence method for the sum of two maximal monotone operators (Recommended article)
Recommended article: On the maximality of the sum of two maximal monotone operators
Similarity Score: 0.9039381
Recommender Run: Recommender Run 3