Interior proximal method for variational inequalities: Case of nonparamonotone operators

DOI10.1007/s11228-004-4379-2zbMath1072.65093OpenAlexW2127315776MaRDI QIDQ1771256

Rainer Tichatschke, Alexander Kaplan

Publication date: 7 April 2005

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-004-4379-2

zbMATH Keywords

convergencemaximal monotone operatorsvariational inequalitiesregularizationconvex programsnonlinear complementarity problemsproximal point methodsBregman distance functionals

Mathematics Subject Classification ID

Convex programming (90C25) Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Numerical methods based on nonlinear programming (49M37) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (4)

A proximal method with logarithmic barrier for nonlinear complementarity problems ⋮ An interior proximal method for a class of quasimonotone variational inequalities ⋮ Interior proximal method without the cutting plane property ⋮ Bregman-like functions and proximal methods for variational problems with nonlinear constraints

Cites Work

• An interior point method for constrained saddle point problems
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• Approximate iterations in Bregman-function-based proximal algorithms
• A logarithmic-quadratic proximal method for variational inequalities
• Pseudomonotone variational inequality problems: Existence of solutions
• Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities
• An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities
• Proximal Point Approach and Approximation of Variational Inequalities
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• Monotone Operators and the Proximal Point Algorithm
• A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space
• Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
• On the Maximality of Sums of Nonlinear Monotone Operators
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