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2007 | 27 | 1 | 71-93
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Interior proximal method for variational inequalities on non-polyhedral sets

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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 analysis of the method studied admits the use of the 𝝐-enlargement of the operator and an inexact solution of the subproblems.
  • Department of Mathematics, University of Trier, 54286 Trier, Germany
  • Department of Mathematics, University of Trier, 54286 Trier, Germany
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