Displaying similar documents to “A Survey on Vector 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...

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

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.

Variational inequalities in noncompact nonconvex regions

Ching-Yan Lin, Liang-Ju Chu (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem...

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2005)

RAIRO - Operations Research - Recherche Opérationnelle

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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are...

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2006)

RAIRO - Operations Research

Similarity:

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space ...

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.