  This paper analyzes the Lipschitz behavior of the feasible set in two
parametric settings, associated with linear and convex systems in R^n. To start
with, we deal with the parameter space of linear (finite/semi-infinite) systems
identified with the corresponding sets of coefficient vectors, which are
assumed to be closed subsets of R^(n+1). In this framework, where the Hausdorff
distance is used to measure the size of perturbations, an explicit formula for
computing the Lipschitz modulus of the feasible set mapping is provided. As
direct antecedent, we appeal to its counterpart in the parameter space of all
linear systems with a fixed index set, T, where the Chebyshev (pseudo) distance
was considered to measure the perturbations. Indeed, the stability (and,
particularly, Lipschitz properties) of linear systems in the Chebyshev
framework has been widely analyzed in the literature. Here, through an
appropriate indexation strategy, we take advantage of previous results to
derive the new ones in the Hausdorff setting. In a second stage, the
possibility of perturbing directly the set of coefficient vectors of a linear
system allows us to provide new contributions on the Lipschitz behavior of
convex systems via linearization techniques.
