A contraction proximal point algorithm with two monotone operators

DOI10.1016/j.na.2012.05.016zbMath1296.47066OpenAlexW2062308098MaRDI QIDQ450610

Oganeditse Aaron Boikanyo, Gheorghe Morosanu

Publication date: 13 September 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.05.016

zbMATH Keywords

strong convergencemaximal monotone operatorresolvent operatornonexpansive mapproximal point algorithmfirmly nonexpansive operatormethod of alternating projectionssubdifferentials of indicator functions

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators ⋮ Iterative methods for a class of variational inequalities in Hilbert spaces ⋮ Solutions for a variational inclusion problem with applications to multiple sets split feasibility problems ⋮ Approximating common fixed points of Bregman weakly relatively nonexpansive mappings in Banach spaces ⋮ Iterative methods for zeros of a monotone variational inclusion in Hilbert spaces ⋮ A generalized contraction proximal point algorithm with two monotone operators

Cites Work

• On the method of alternating resolvents
• A proximal point algorithm converging strongly for general errors
• Four parameter proximal point algorithms
• Inexact Halpern-type proximal point algorithm
• The asymptotic behavior of the composition of two resolvents
• A regularization method for the proximal point algorithm
• On convergence criteria of generalized proximal point algorithms
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Projection and proximal point methods: Convergence results and counterexamples.
• Approximating solutions of maximal monotone operators in Hilbert spaces
• An alternating projection that does not converge in norm
• Iterative Algorithms for Nonlinear Operators
• The Method of Alternating Resolvents Revisited
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item