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This paper analyzes the Lipschitz behavior of the feasible set in twoparametric settings, associated with linear and convex systems in R^n. To startwith, we deal with the parameter space of linear (finite/semi-infinite) systemsidentified with the corresponding sets of coefficient vectors, which areassumed to be closed subsets of R^(n+1). In this framework, where the Hausdorffdistance is used to measure the size of perturbations, an explicit formula forcomputing the Lipschitz modulus of the feasible set mapping is provided. Asdirect antecedent, we appeal to its counterpart in the parameter space of alllinear systems with a fixed index set, T, where the Chebyshev (pseudo) distancewas considered to measure the perturbations. Indeed, the stability (and,particularly, Lipschitz properties) of linear systems in the Chebyshevframework has been widely analyzed in the literature. Here, through anappropriate indexation strategy, we take advantage of previous results toderive the new ones in the Hausdorff setting. In a second stage, thepossibility of perturbing directly the set of coefficient vectors of a linearsystem allows us to provide new contributions on the Lipschitz behavior ofconvex systems via linearization techniques.

Lipschitz modulus of linear and convex systems with the Hausdorff metric