Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

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

Abstrakty

EN

In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.

Słowa kluczowe

EN

variational inequalities; Bregman function; non-polyhedral feasible set; proximal point 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: 2010
• Tom: 30
• Numer: 1
• Strony: 51-59

Daty

wydano

2010

otrzymano

2008-10-23

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

• [1] A. Auslender and M. Haddou, An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities, Math. Programming 71 (1995), 77-100. doi:10.1007/BF01592246
• [2] A. Auslender and M. Teboulle, Entropic proximal decomposition methods for convex programs and variational inequalities, Math. Programming (A) 91 (2001), 33-47.
• [3] A. Auslender, M. Teboulle and S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Computational Optimization and Applications 12 (1999), 31-40. doi:10.1023/A:1008607511915
• [4] Y. Censor, A. Iusem and S.A. Zenios, An interior point method with Bregman functions for the variational inequality problem with paramonotone operators, Math. Programming 81 (1998), 373-400. doi:10.1007/BF01580089
• [5] A. Kaplan and R. Tichatschke, Interior proximal method for variational inequalities: Case of non-paramonotone operators, Journal of Set-valued Analysis 12 (2004), 357-382. doi:10.1007/s11228-004-4379-2
• [6] A. Kaplan and R. Tichatschke, Interior proximal method for variational inequalities on non-polyhedral sets, Discuss. Math. DICO 27 (2007), 71-93.

Identyfikatory

DOI

10.7151/dmdico.1111