Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

As very powerful and important tools in the study of nonlinear sciences, variational inequalities and vector optimization have attracted so much attention. Over the last decades, variational inequality and vector optimization techniques have been applied extensively in such diverse fields as biology, chemistry, economics, engineering, game theory, management science, physics, and so on. The tho...

In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...

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...

In this paper, we introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of vector variational inequality and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problem...

In this paper we survey the relationships between scalar and vector variational inequalities (of differential type) and the underlying optimization problem. We show that the variational inequalities of Stampacchia type can be viewed as necessary optimality conditions, while the variational inequalities of Minty type can be considered as sufficient optimality conditions. Concerning this last sta...

In this paper, we consider and study a class of vector variational-like inequalities in Banach space without any generalized monotonicity by exploiting vector version of minimax inequality and obtain the existence results of solutions to the class of vector variational-like inequalities. The results presented here are different from [1, 5, 11], and extend and generalize the corresponding result...

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 analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.