Approximate proximal point algorithms for finding zeroes of maximal monotone operators in Hilbert spaces

DOI10.1155/2008/598191zbMath1153.47052OpenAlexW2031929276WikidataQ59214274 ScholiaQ59214274MaRDI QIDQ938427

Kang, Shin Min, Hai-Yun Zhou, Yeol Je Cho

Publication date: 19 August 2008

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

Full work available at URL: https://eudml.org/doc/129549

zbMATH Keywords

maximal monotone operatorproximal point algorithmminimizer for a convex function

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Set-valued operators (47H04)

Related Items (16)

Iterative algorithms for infinite accretive mappings and applications to \(p\)-Laplacian-like differential systems ⋮ Some new iterative algorithms with errors for common solutions of two finite families of accretive mappings in a Banach space ⋮ Strong and weak convergence theorems for common zeros of finite accretive mappings ⋮ Strong convergence of iterative schemes for zeros of accretive operators in reflexive Banach spaces ⋮ Best proximity points of non-self mappings ⋮ Approximating zeros of monotone operators by proximal point algorithms ⋮ Iterative algorithms for common elements in fixed point sets and zero point sets with applications ⋮ Strong convergence of a hybrid projection iterative algorithm for common solutions of operator equations and of inclusion problems ⋮ Convergence results for the zero-finding problem and fixed points of nonexpansive semigroups and strict pseudocontractions ⋮ Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces ⋮ Iterative approaches to find zeros of maximal monotone operators by hybrid approximate proximal point methods ⋮ Convergence of an iterative algorithm for common solutions for zeros of maximal accretive operator with applications ⋮ Iterative scheme with errors for common zeros of finite accretive mappings and nonlinear elliptic systems ⋮ On weak convergence of an iterative algorithm for common solutions of inclusion problems and fixed point problems in Hilbert spaces ⋮ Iterative schemes for approximating solution of nonlinear operators in Banach spaces ⋮ Convergence theorems for maximal monotone operators, weak relatively nonexpansive mappings and equilibrium problems

Cites Work

• Approximate iterations in Bregman-function-based proximal algorithms
• A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Iterative Algorithms for Nonlinear Operators
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Monotone Operators and the Proximal Point Algorithm

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