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

Alexander Kaplan; Rainer Tichatschke

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 1, page 51-59
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Alexander Kaplan, and Rainer Tichatschke. "Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.1 (2010): 51-59. <http://eudml.org/doc/271150>.

@article{AlexanderKaplan2010,
abstract = {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.},
author = {Alexander Kaplan, Rainer Tichatschke},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {variational inequalities; Bregman function; non-polyhedral feasible set; proximal point algorithm},
language = {eng},
number = {1},
pages = {51-59},
title = {Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets},
url = {http://eudml.org/doc/271150},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Alexander Kaplan
AU - Rainer Tichatschke
TI - Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 1
SP - 51
EP - 59
AB - 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.
LA - eng
KW - variational inequalities; Bregman function; non-polyhedral feasible set; proximal point algorithm
UR - http://eudml.org/doc/271150
ER -

References

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  1. [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 Zbl0855.90095
  2. [2] A. Auslender and M. Teboulle, Entropic proximal decomposition methods for convex programs and variational inequalities, Math. Programming (A) 91 (2001), 33-47. Zbl1051.90017
  3. [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 Zbl1039.90529
  4. [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. [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 Zbl1072.65093
  6. [6] A. Kaplan and R. Tichatschke, Interior proximal method for variational inequalities on non-polyhedral sets, Discuss. Math. DICO 27 (2007), 71-93. Zbl1158.47052

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