Proximal projection methods for variational inequalities and Cesáro averaged approximations

DOI10.1016/S0898-1221(02)80016-5zbMath1050.65065OpenAlexW2058693999MaRDI QIDQ1876480

Ya. I. Al'ber

Publication date: 20 August 2004

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(02)80016-5

zbMATH Keywords

Lyapunov functionalsBanach spaceStabilityVariational inequalityMonotone operatorsCesáro averaged convergenceMetric and generalized projection operatorsNormalized duality mappingProx-projection methodYoung-Fenchel transformation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Newton-type methods (49M15)

Related Items

The connection between the metric and generalized projection operators in Banach spaces ⋮ A strong convergence theorem for relatively nonexpansive mappings and equilibrium problems in Banach spaces ⋮ Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces ⋮ The generalized \(f\)-projection operator and set-valued variational inequalities in Banach spaces ⋮ Properties of the generalized \(f\)-projection operator and its applications in Banach spaces ⋮ The generalized projection operator on reflexive Banach spaces and its applications ⋮ Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces ⋮ The generalised f-projection operator with an application

Cites Work

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• Nonlinear Ill-posed Problems of Monotone Type
• Monotone Operators and the Proximal Point Algorithm
• On a proximal point method for convex optimization in banach spaces
• On the convergence of the proximal algorithm for saddle-point problems
• The penalty method for variational ineqalities with nonsmooth unbounded operators in banach space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Generalized Projection Operators in Banach Spaces: Properties and Applications
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