Role of relative \(A\)-maximal monotonicity in overrelaxed proximal-point algorithms with Applications

DOI10.1007/s10957-009-9554-zzbMath1178.49006OpenAlexW2092185228MaRDI QIDQ1039359

Ravi P. Agarwal, Ram U. Verma

Publication date: 27 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/s10957-009-9554-z

zbMATH Keywords

maximal monotone mappingvariational inclusionsgeneralized resolvent operatorrelative \(A\)-maximal monotone mapping

Mathematics Subject Classification ID

Variational inequalities (49J40) Fixed-point theorems (47H10)

Related Items (8)

Graph-convergent analysis of over-relaxed \((A, \eta, m)\)-proximal point iterative methods with errors for general nonlinear operator equations ⋮ Revisit the over-relaxed proximal point algorithm ⋮ Convergence analysis of new over-relaxed proximal point algorithm frameworks with errors and applications to general \( A\)-monotone nonlinear inclusion forms ⋮ About the relaxed cocoercivity and the convergence of the proximal point algorithm ⋮ General over-relaxed proximal point algorithm involving \(A\)-maximal relaxed monotone mappings with applications ⋮ Relatively inexact proximal point algorithm and linear convergence analysis ⋮ The generalized relaxed proximal point algorithm involving A-maximal-relaxed accretive mappings with applications to Banach spaces ⋮ A new relaxed proximal point procedure and applications to nonlinear variational inclusions

Cites Work

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• On a new system of nonlinear \(A\)-monotone multivalued variational inclusions
• \(A\)-monotonicity and its role in nonlinear variational inclusions
• Super-relaxed \((\eta)\)-proximal point algorithms, relaxed \((\eta)\)-proximal point algorithms, linear convergence analysis, and nonlinear variational inclusions
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Composition duality and maximal monotonicity
• Finding a zero of the sum of two maximal monotone operators
• Mixed equilibrium problems: sensitivity analysis and algorithmic aspect.
• Generalized over-relaxed proximal algorithm based ona-maximal monotonicity framework and applications to inclusion problems
• A-monotone nonlinear relaxed cocoercive variational inclusions
• Approximation solvability of a class of nonlinear set-valued variational inclusions involving \((A,\eta )\)-monotone mappings
• Nonlinear semigroups in Hilbert space
• General system of \((A,\eta )\)-monotone variational inclusion problems based on generalized hybrid iterative algorithm
• On the differentiability and the representation of one-parameter semi-group of linear operators
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities

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