Displaying similar documents to “Prox-regularization and solution of ill-posed elliptic variational inequalities”

Interior proximal method for variational inequalities on non-polyhedral sets

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...

Application of relaxation scheme to degenerate variational inequalities

Jela Babušíková (2001)

Applications of Mathematics

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In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.

A Survey on Vector Variational Inequalities

F. Giannessi, G. Matroeni, X. Q. Yang (2009)

Bollettino dell'Unione Matematica Italiana

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The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation...