Lispchitz modulus of the argmin mapping in convex quadratic optimization

TL;DR

This paper derives a point-based formula for the Lipschitz modulus of the argmin mapping in convex quadratic optimization, extending previous linear programming results and applicable to perturbed convex quadratic problems.

Contribution

It introduces a novel point-based formula for the Lipschitz modulus of the argmin mapping in convex quadratic problems, generalizing earlier linear programming findings.

Findings

Provides a formula for the Lipschitz modulus of the argmin mapping.

Extends linear programming results to convex quadratic optimization.

Offers a point-based formula for the metric projection on polyhedral convex sets.

Abstract

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.