Seminario 17/08: Michel Théra (U. Limoges) – Perturbation of error bounds

Información

Abstract

In the current presentation, I intend to extend the developments in Kruger, Ngai  & Théra, SIAM J. Optim. 20(6), 3280-3296 (2010) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by proper lower semicontinuous under data perturbations. I will propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the ‘radius of error bounds’. The definitions and characterizations are illustrated by examples. This presentation summarizes recent joint works  with Huynh Van Ngai, Marco López Cerdá  and A. Kruger.