Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal monotone operators

DOI10.1007/s10957-009-9538-zzbMath1180.90334OpenAlexW2075317557MaRDI QIDQ1035944

Jen-Chih Yao, Lu-Chuan Ceng, Giandomenico Mastroeni

Publication date: 4 November 2009

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

Full work available at URL: https://doi.org/10.1007/s10957-009-9538-z

zbMATH Keywords

Banach spacesstrong convergenceweak convergenceequilibrium problemsmonotone mappingscommon solutionshybrid proximal point type methodsmulti-valued inclusions

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Numerical methods for variational inequalities and related problems (65K15) Variational and other types of inclusions (47J22)

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Cites Work

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• Modified proximal-point algorithm for maximal monotone operators in Banach spaces
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Weak and strong convergence theorems for maximal monotone operators in a Banach space
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• An inexact proximal-type algorithm in Banach spaces
• A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
• Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• On the projection methods for fixed point problems
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Inequalities in Banach spaces with applications
• Monotone Operators and the Proximal Point Algorithm
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications