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2010 | 30 | 1 | 51-59
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Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

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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.
Twórcy
  • Department of Mathematics, University of Trier, 54286 Trier, Germany
  • 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.
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Bibliografia
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