This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinear function based on a well-known nonlinear scalarization function. We...

The aim of this paper is to consider time-dependent variational and quasi-variational inequalities and to study under which assumptions the continuity of solutions with respect to the time can be ensured. Making on appropriate use of the set convergence in Mosco’s sense, we get the desiderate continuity results for strongly monotone variational and quasi-variational inequalities. The continuity...

The purpose of this paper is to introduce the concept of fuzzy variational-like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational-like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan’s KKM theorem, Nadler’s fixed point theorem, and some new analytic techniques, so...

In this paper, we consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known res...

In [8] the notion of “projected differential equation” has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in [20], Minty variational inequalities have been involved in the study of properties of the trajectories of such a projected differential equation. We consider classical generalizations of both problems,...

This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

In this paper, we introduce and study a new class of generalized nonlinear mixed quasi-variational inequalities involving maximal η-monotone mapping. Using the resolvent operator technique for maximal η-monotone mapping, we prove the existence of solution for this kind of generalized nonlinear multi-valued mixed quasi-variational inequalities without compactness and the convergence of iterative...

This paper is a continuation of our previous paper [3] were we presented generalizations of the Dennis-Moré theorem to characterize q-superliner convergences of quasi-Newton methods for solving equations and variational inequalities in Banach spaces. Here we prove Dennis-Moré type theorems for inexact quasi-Newton methods applied to variational inequalities in finite dimensions. We first consid...

*Correspondence: [email protected] School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China Abstract This paper introduces the notion of exceptional family of elements for generalized variational inequalities in Hilbert spaces. The set-valued mapping is assumed to be upper semi-continuous compact with nonempty closed convex values. Based on topological deg...

Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see text]; (2) the set of solutions of this system of multivariate variational inequalities is close...