Interior proximal method for variational inequalities on non-polyhedral sets

• Autorzy: Alexander Kaplan , Rainer Tichatschke
• Języki publikacji: EN

Abstrakty

EN

Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of the method studied admits the use of the 𝝐-enlargement of the operator and an inexact solution of the subproblems.

Słowa kluczowe

EN

variational inequalities; Bregman function; proximal algorithm

Kategorie tematyczne

• 47J20: Variational and other types of inequalities involving nonlinear operators (general)
• 47H05: Monotone operators and generalizations
• 65K10: Optimization and variational techniques
• 65J20: Improperly posed problems; regularization
• 90C25: Convex programming

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 71-93

Daty

wydano

2007

otrzymano

2006-02-16

Twórcy

autor

Alexander Kaplan

• Department of Mathematics, University of Trier, 54286 Trier, Germany

autor

Rainer Tichatschke

• Department of Mathematics, University of Trier, 54286 Trier, Germany

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico1077