Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators
From MaRDI portal
Publication:1265027
DOI10.1023/A:1022646327085zbMath0908.90209MaRDI QIDQ1265027
S. Haubruge, Van Hien Nguyen, Jean Jacques Strodiot
Publication date: 28 February 1999
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
maximal monotone operatorsvariational inequalitiesconvex programssplitting method\(\theta\)-schemeparallel optimization
Related Items
Some recent advances in projection-type methods for variational inequalities ⋮ Some developments in general variational inequalities ⋮ New trends in general variational inequalities ⋮ Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators ⋮ Fixed point approximation of asymptotically nonexpansive mappings in hyperbolic spaces ⋮ On Noor-type iteration schemes for multivalued mappings in \(\mathrm{CAT}(0)\) spaces ⋮ A reconsideration on convergence of three-step iterations for asymptotically nonexpansive mappings ⋮ Some new results on three-step iterations with errors for strongly successively pseudocontractions ⋮ Construction algorithms for a class of monotone variational inequalities ⋮ A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings ⋮ Modified multistep iterative process for some common fixed point of a finite family of nonself asymptotically nonexpansive mappings ⋮ Modified Noor iterations for nonlinear equations in Banach spaces ⋮ Unnamed Item ⋮ The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces ⋮ Convergence of three-step iterations for asymptotically nonexpansive mappings ⋮ A new modified three-step iteration method for G-nonexpansive mappings in Banach spaces with a graph ⋮ Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings ⋮ Three step iterative algorithms for solving a class of quasi variational inequalities ⋮ Convergence analysis of M-iteration for \(\mathcal{G}\)-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems ⋮ Mixed-type SP-iteration for asymptotically nonexpansive mappings in hyperbolic spaces ⋮ Convergence point of G-nonexpansive mappings in Banach spaces endowed with graphs applicable in image deblurring and signal recovering problems ⋮ The Glowinski-Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces ⋮ Unnamed Item ⋮ Fixed point approximation of nonexpansive mappings on a nonlinear domain ⋮ The Glowinski-Le Tallec splitting method revisited: a general convergence and convergence rate analysis ⋮ A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly $L$--Lipschitzian Asymptotically Generalized $\Phi$-Hemicontractive Mappings ⋮ Strong convergence theorems for three-step iterations with errors for non-Lipschitzian nonself-mappings in Banach spaces ⋮ Demiclosed principle and convergence for modified three step iterative process with errors of non-Lipschitzian mappings ⋮ Convergence and stability of a three-step iterative algorithm for a general quasi-variational inequality problem ⋮ Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces ⋮ Modified resolvent splitting algorithms for general mixed variational inequalities ⋮ Some resolvent iterative methods for variational inclusions and nonexpansive mappings ⋮ Equivalence results for implicit Jungck–Kirk type iterations ⋮ Unnamed Item ⋮ Projection-splitting algorithms for monotone variational inequalities ⋮ Self-adaptive projection algorithms for general variational inequalities ⋮ Splitting methods for pseudomonotone mixed variational inequalities ⋮ Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings ⋮ Iterative computation for solving the variational inequality and the generalized equilibrium problem ⋮ New approximation schemes for general variational inequalities ⋮ RELAXED Η-PROXIMAL OPERATOR FOR SOLVING A VARIATIONAL-LIKE INCLUSION PROBLEM ⋮ Three-step iterations for total asymptotically nonexpansive mappings in CAT(0) spaces ⋮ Three-step iterations for nonlinear accretive operator equations ⋮ Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces ⋮ Convergence of three-step iterations for nearly asymptotically nonexpansive mappings in \(\operatorname{CAT}(k)\) spaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- A proximal-based deomposition method for compositions method for convex minimization problems
- A parallel descent algorithm for convex programming
- Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- A Perturbed Parallel Decomposition Method for a Class of Nonsmooth Convex Minimization Problems
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
- Monotone Operators and the Proximal Point Algorithm
- Convex Functions with Unbounded Level Sets and Applications to Duality Theory
- Proximal Decomposition on the Graph of a Maximal Monotone Operator
- Asymptotic Convergence Analysis of the Forward-Backward Splitting Algorithm
- Convex Analysis
- On the Maximality of Sums of Nonlinear Monotone Operators