M. J. Cánovas (Center of Operations Research, Miguel Hernández University of Elche) and J. Parra (Center of Operations Research, Miguel Hernández University of Elche)


This paper is intended to provide an overview of recent results by the authors, together with different collaborators, on quantitative measures of the Lispchitzian behavior of the feasible and the optimal (argmin) sets in continuous linear semi-infinite optimization (with a finite amount of variables and possibly infinitely many constraints). Specifically, the paper focuses on the computation of the global Hoffman constant for the feasible set mapping as well as the Lipschitz and calmness moduli for both the feasible and the optimal set mappings. We point out the fact that all these measures are computed through point-based formulae; i.e., only involving the problem’s data, not appealing to elements in a neighborhood. Hence, the computation of such measures is conceptually implementable in practice. The difficulties appearing in contrast to the finite setting (with finitely many constraints) is highlighted. On that basis, to the authors knowledge, this work presents the state of the art on the point-based computation of the referred measures in the context of linear semi-infinite optimization, with an incursion into infinite-dimensional spaces of variables.