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Ram U. Verma (1998)
Commentationes Mathematicae Universitatis Carolinae
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The solvability of a class of monotone nonlinear variational inequality problems in a reflexive Banach space setting is presented.
Alexander Kaplan, Rainer Tichatschke (2007)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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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...
Alexander Kaplan, Rainer Tichatschke (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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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.
Fulina, Silvia (2006)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Verma, Ram U. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Oppezzi, Pirro, Rossi, Anna Maria (1995)
Journal of Convex Analysis
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Leonid D. Popov (2001)
The Yugoslav Journal of Operations Research
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Plubtieng, Somyot, Sombut, Kamonrat (2010)
Journal of Inequalities and Applications [electronic only]
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Alber, Y.I., Kartsatos, A.G., Litsyn, E. (1996)
Abstract and Applied Analysis
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Mohammad Chowdhury, Kok-Keong Tan (2008)
Open Mathematics
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Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.