Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

DOI10.1080/01630563.2018.1424201zbMath1479.47080OpenAlexW2781478074MaRDI QIDQ4643756

Chih-Sheng Chuang, Lai-Jiu Lin, Zenn-Tsuen Yu

Publication date: 28 May 2018

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2018.1424201

zbMATH Keywords

strong convergencevariational inequalityminimization problemlinear inverse problemsplit feasibility problemstrongly monotone mapping

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Iterative procedures involving nonlinear operators (47J25) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)

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Strong convergence theorem for common zero points of inverse strongly monotone mappings and common fixed points of generalized demimetric mappings ⋮ Outer Approximation Methods for Solving Variational Inequalities Defined over the Solution Set of a Split Convex Feasibility Problem

Cites Work

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• Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications
• Iterative approximation of solutions for proximal split feasibility problems
• Self-adaptive algorithms for proximal split feasibility problems and strong convergence analysis
• Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings
• Fixed point optimization algorithm and its application to power control in CDMA data networks
• Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces
• The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces
• A general iterative algorithm for nonexpansive mappings in Hilbert spaces
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Quelques propriétés des opérateurs angle-bornes et n-cycliquement monotones
• The common fixed point theory of singlevalued mappings and multivalued mappings
• A multiprojection algorithm using Bregman projections in a product space
• Totally convex functions for fixed points computation and infinite dimensional optimization
• Convergence of generalized proximal point algorithms
• Viscosity approximation methods for nonexpansive mappings
• Viscosity approximation methods for fixed-points problems
• Mathematical programming with multiple sets split monotone variational inclusion constraints
• A general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces
• A general iterative method for nonexpansive mappings in Hilbert spaces
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• Fixed point optimization algorithm and its application to network bandwidth allocation
• Computational Method for Solving a Stochastic Linear-Quadratic Control Problem Given an Unsolvable Stochastic Algebraic Riccati Equation
• Application of Quasi-Nonexpansive Operators to an Iterative Method for Variational Inequality
• Robust Wideband Beamforming by the Hybrid Steepest Descent Method
• Solving monotone inclusions via compositions of nonexpansive averaged operators
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
• A block-iterative surrogate constraint splitting method for quadratic signal recovery
• Signal Recovery by Proximal Forward-Backward Splitting
• Convex analysis and monotone operator theory in Hilbert spaces