Multi-step extragradient method with regularization for triple hierarchical variational inequalities with variational inclusion and split feasibility constraints

DOI10.1186/1029-242X-2014-492zbMath1334.49023OpenAlexW2126023531WikidataQ59323298 ScholiaQ59323298MaRDI QIDQ261793

Ching-Feng Wen, Chin-Tzong Pang, Lu-Chuan Ceng

Publication date: 24 March 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2014-492

zbMATH Keywords

iterative algorithmstrong convergencevariational inclusionsfixed point problemssplit feasibility problemstriple hierarchical variational inequalities

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Numerical methods based on necessary conditions (49M05) Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Set-valued operators (47H04) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical methods for variational inequalities and related problems (65K15) Variational and other types of inclusions (47J22)

Related Items

A modified Ishikawa iteration scheme for b‐enriched nonexpansive mapping to solve split variational inclusion problem and fixed point problem in Hilbert spaces ⋮ A new iterative algorithm for the multiple-sets split feasibility problem and the split equality fixed point problem ⋮ Composite relaxed extragradient method for triple hierarchical variational inequalities with constraints of systems of variational inequalities ⋮ Hybrid implicit steepest-descent methods for triple hierarchical variational inequalities with hierarchical variational inequality constraints ⋮ Modified inertial subgradient extragradient algorithms for pseudomonotone equilibrium problems with the constraint of nonexpansive mappings ⋮ Quasi-Inertial Tseng’s Extragradient Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Quasi-Nonexpansive Operators ⋮ Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings ⋮ New subgradient extragradient methods for solving monotone bilevel equilibrium problems ⋮ Composite steepest-descent method for the triple hierarchical variational inequalities

Cites Work

• Multistep hybrid extragradient method for triple hierarchical variational inequalities
• Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem
• Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems
• Convergence of hybrid steepest-descent methods for variational inequalities
• Relaxed extragradient iterative methods for variational inequalities
• An extragradient method for solving split feasibility and fixed point problems
• Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method
• Characterization of \(H\)-monotone operators with applications to variational inclusions
• Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space
• Existence theory for finite-dimensional pseudomonotone equilibrium problems
• A new completely general class of variational inclusions with noncompact valued mappings
• Algorithms of common solutions for generalized mixed equilibria, variational inclusions, and constrained convex minimization
• Equilibrium problems under generalized convexity and generalized monotonicity
• The existence of nonlinear inequalities
• Solving non-additive traffic assignment problems: a descent method for co-coercive variational inequalities
• A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Generalized monotone bifunctions and equilibrium problems
• Existence Theorems for Generalized Noncoercive Equilibrium Problems: The Quasi-Convex Case
• Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization
• Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces
• Iterative Algorithms for Nonlinear Operators
• Monotone Operators and the Proximal Point Algorithm
• A unified treatment of some iterative algorithms in signal processing and image reconstruction
• Iterative oblique projection onto convex sets and the split feasibility problem
• Solving monotone inclusions via compositions of nonexpansive averaged operators
• Triple Hierarchical Variational Inequalities
• Split Feasibility and Fixed Point Problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item