Perturbation Theory of Polyhedral Seminorms Under Linear Constraints

Abstract

A recent paper by Klatte and Kummer provides a new characterization for the regularity of the $\argmin$ set of an optimization problem with respect to perturbations. In this thesis we prove that this characterization applies to a broad class of widely used minimization problems. In particular, this work applies to both $\ell_1$ and (anisotropic) discrete total variation minimization problems under linear constraints.