An operator splitting method for variational inequalities with partially unknown mappings

DOI10.1007/s00211-008-0181-7zbMath1159.65069OpenAlexW1975101135MaRDI QIDQ998631

Deren Han, Hai Yang, Wei Xu

Publication date: 9 February 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-008-0181-7

zbMATH Keywords

global convergencesystem of nonlinear equationsvariational inequalitynumerical examplesoperator splitting methodself-adaptive strategy

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Discrete approximations in optimal control (49M25)

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Cites Work

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• Inexact operator splitting methods with selfadaptive strategy for variational inequality problems
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Error bounds in mathematical programming
• A new method for a class of nonlinear variational inequalities with fuzzy mappings
• Self-adaptive operator splitting methods for monotone variational inequalities
• A new modified Goldstein-Levitin-Polyak projection method for variational inequality problems
• Inexact implicit methods for monotone general variational inequalities
• The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Monotone Operators and the Proximal Point Algorithm
• Computing stationary points
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Network economics. A variational inequality approach.
• Modified Goldstein--Levitin--Polyak projection method for asymmetric strongly monotone variational inequalities