We study regularity properties of the subdifferential of proper lower semicontinuous convex functions
in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the strong
regularity and subregularity of such a subdifferential. We characterize each of these properties…

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of
perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the…

This paper analyzes inequality systems with an arbitrary number of proper lower semicontinuous convex
constraint functions and a closed convex constraint subset of a locally convex topological vector space.
More in detail, starting from well-known results on linear systems (with…

The evenly convex hull of a given set is the intersection of all the open halfspaces
which contain such set (hence the convex hull is contained in the evenly convex hull). This paper
deals with finite dimensional linear systems containing…

This paper deals with the transmission of the main stability properties (lower and
upper semicontinuity in Berge sense, and closedness) from a given closed–convex-valued mapping to
its corresponding relative boundary and extreme point set mappings, and vice versa. The domain

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying…