Extended auxiliary problem principle using Bregman distances

DOI10.1080/02331930412331326301zbMath1153.49303OpenAlexW2007138582MaRDI QIDQ4669792

Alexander Kaplan, Rainer Tichatschke

Publication date: 15 April 2005

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930412331326301

zbMATH Keywords

Variational inequalitiesBregman distancesAuxiliary problem principleProximal-like regularization

Mathematics Subject Classification ID

Convex programming (90C25) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (3)

Maximum entropy estimation for survey sampling ⋮ Bregman-like functions and proximal methods for variational problems with nonlinear constraints ⋮ Bregman functions and auxiliary problem principle

Cites Work

• Convergence analysis of non-quadratic proximal methods for variational inequalities in Hilbert spaces
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• Solution of variational inequalities in mechanics
• Complementarity problems over cones with monotone and pseudomonotone maps
• Progressive regularization of variational inequalities and decomposition algorithms
• Approximate iterations in Bregman-function-based proximal algorithms
• Enlargement of monotone operators with applications to variational inequalities
• A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
• Coupling the auxiliary problem principle and epiconvergence theory to solve general variational inequalities
• \(\varepsilon\)-enlargements of maximal monotone operators in Banach spaces
• Family of perturbation methods for variational inequalities
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators
• On inexact generalized proximal methods with a weakened error tolerance criterion
• Extended auxiliary problem principle to variational inequalities involving multi-valued operators

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