Perturbation of error bounds

SEMINARIO DEL DOCTORADO DE ESTADÍSTICA, OPTIMIZACIÓN Y MATEMÁTICA APLICADA. CURSO 2016-2017

Título: Perturbation of error bounds

Ponentes: Michel Théra (University of Limoges, France)

Fecha: Viernes 24 de marzo de 2017 a las 12:30 horas

Lugar: Sala de seminarios, Instituto Universitario de Investigación CIO, Edificio Torretamarit, Universidad Miguel Hernández (Campus de Elche)

Resumen:

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.