arXiv subjects

María Josefa Cánovas

Publications and source records attributed to María Josefa Cánovas.

3 recordsLinked to original sources

arXiv2025

Lispchitz modulus of the argmin mapping in convex quadratic optimization

This paper was initially motivated by the computation of the Lipschitz modulus of the metric projection on polyhedral convex sets in the Euclidean space when both the reference point and the polyhedron where it is projected are subject to perturbations. The paper tackles the more general problem of computing the Lipschitz modulus of the argmin mapping in the framework of canonically perturbed convex quadratic problems. We point out the fact that a point-based formula (depending only on the nominal data) for such a modulus is provided. In this way, the paper extends to the current quadratic setting some results previously developed in linear programming. As an application, we provide a point-based formula for the Lipschitz modulus of the metric projection on a polyhedral convex set.

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arXiv2025

Lipschitz upper semicontinuity of linear inequality systems under full perturbations

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full vs RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [A. J. HOFFMAN, J. Res. Natl. Bur. Stand. 49 (1952), pp. 263--265] and Robinson [S. M. ROBINSON, Math. Progr. Study 14 (1981), pp. 206--214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyze the Lipschitz upper semicontinuity property and its corresponding modulus.

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arXiv2022

From calmness to Hoffman constants for linear semi-infinite inequality systems

In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand side. The Hoffman modulus is shown to coincide with the supremum of Lipschitz upper semicontinuity and calmness moduli when confined to multifunctions with a convex graph and closed images in a reflexive Banach space, which is the case of our feasible set mapping. Moreover, for this particular multifunction a formula -- only involving the system's left-hand side -- of the global Hoffman constant is derived, providing a generalization to our semi-infinite context of finite counterparts developed in the literature. In the particular case of locally polyhedral systems, the paper also provides a point-based formula for the (semi-local) Hoffman modulus in terms of the calmness moduli at certain feasible points (extreme points when the nominal feasible set contains no lines), yielding a practically tractable expression for finite systems.

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