A parametric version of the Borwein-Preiss smooth variational principle is presented, which states that under suitable assumptions on a given convex function depending on a parameter, the minimum point of a smooth convex perturbation of it depends continuously on the parameter. Some applications are given: existence of a Nash equilibrium and a solution of a variational inequality for a system o...

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi 1995, 1996 for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is ...

We analyze the nite element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed 31], and existence and uniqueness results for this problem have been given there. In this contribution the same approach ...

Variational inequality modeling, analysis and computations are important for many applications, but most of the subject has been developed in a deterministic setting with no uncertainty in a problem’s data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on a rather limited idea of what a stochastic variation...

The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle brings also quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.

The theory of evolutionary variational inequalities fits very well in a lot of optimization problems, like for example the dynamic oligopolistic market equilibrium problem that we describe in this paper. But here, the authors analyze the behavior of control policies whose aim is to regulate the exportation through the adjustments of supply taxes or incentives on the firms. This is considered as...

Variational inequality methods whether based on numerous available new algorithms or otherwise have been applied vigorously, especially to model equilibria problems in economics, optimization and control theory, operations research, transportation network modeling, and mathematical programming, while a considerable progress to developing general methods for the sensitivity analysis for variatio...

In this paper we give an elementary introduction into the theory of variational inequalities and their application to general equilibrium analysis. Furthermore we incorporate some results on sensitivity analysis of variational inequalities on polyhe-dral sets.

The purpose of this paper is to introduce and study a new class of generalized vector variational-like inequalities and generalized vector variational inequalities in fuzzy environment. By using the KKM-technique, Maximal Element Lemma and under suitable conditions, some existence theorems of solutions for these two kinds of vector variational inequalities in fuzzy environment are proved. The r...