A general framework for the over-relaxed A-proximal point algorithm and applications to inclusion problems

DOI10.1016/J.AML.2008.05.001zbMath1183.47074OpenAlexW1972137641MaRDI QIDQ1021801

Ram U. Verma

Publication date: 9 June 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2008.05.001

zbMATH Keywords

maximal monotone mappingvariational inclusionsgeneralized resolvent operatorover-relaxed \(A\)-proximal point algorithm\(A\)-maximal monotone mapping

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25)

Related Items (9)

The over-relaxed scheme based on \(H(\cdot ,\cdot )\)-cocoercive operators for solving a generalized variational inclusion problem ⋮ Graph-convergent analysis of over-relaxed \((A, \eta, m)\)-proximal point iterative methods with errors for general nonlinear operator equations ⋮ On over-relaxed \((A,{\eta},m)\)-proximal point algorithm frameworks with errors and applications to general variational inclusion problems ⋮ Convergence analysis of new over-relaxed proximal point algorithm frameworks with errors and applications to general \( A\)-monotone nonlinear inclusion forms ⋮ Unnamed Item ⋮ Total asymptotically nonexpansive mappings and generalized variational-like inclusion problems in semi-inner product spaces ⋮ The over-relaxed \(A\)-proximal point algorithm for general nonlinear mixed set-valued inclusion framework ⋮ General system of \((A,\eta )\)-maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms ⋮ General implicit variational inclusion problems based on \(A\)-maximal (\(m\))-relaxed monotonicity (AMRM) frameworks

Cites Work

• On a new system of nonlinear \(A\)-monotone multivalued variational inclusions
• \(A\)-monotonicity and its role in nonlinear variational inclusions
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Approximation solvability of a class of nonlinear set-valued variational inclusions involving \((A,\eta )\)-monotone mappings
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity
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