The Role of "Monotonicity" for Approximation andStability of Vector Quasi-Variational Inequalities

Various concepts of exact and approximate solutions for vector quasivariationalinequalities are presented.Related well-posedness and stability results are illustrated, enlightening the key role played in this investigationby "monotonicity" of operators and by "convexity" of set-valuedmappings

Approximate solutions to variational inequalities and applications

The aim of this paper is to investigate two concepts of approximate solutions to parametric variational inequalities in topological vector spaces for which the corresponding solution map is closed graph and/or lower semicontinuous and to apply the results to the stability of optimization problems with variational inequality constrains

Asymptotic Behavior of Semi-quasivariational Optimistic Bilevel Problems in Banach Spaces

The great interest into hierarchical optimization problems and the increasing use of game theory in many economic or engineering applications led to investigate scalar bilevel problems in which the upper level is an optimization problem and the lower level is a parametrized quasi-variational inequality. In this paper, we analyze the convergence of the sequences of infima and minima for the upper level when the data of the problem are perturbed. First, we show that general results on the convergence of the infima and minima may not be possible. Thus, we introduce suitable concepts of regularized semi-quasivariational optimistic bilevel problems and we study, in Banach spaces, the convergence properties of the infima and minima to these regularized problems in the presence or not of perturbations

Continuous convergence and preservation of convergences of sets

AbstractA systematic study of convergence of images of families of relation is undertaken. Structurally these are questions from the theory of continuous convergence