A convex approach to differential inclusions with prox-regular sets

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

Título: A convex approach to differential inclusions with prox-regular sets

Ponentes: Dr. Abderrahim Hantoute (Center for Mathematical Modeling, University of Chile)

Fecha: Martes 13 de junio de 2017 a las 18:30 horas

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

Resumen:

We study the existence and stability of the solutions for differential inclusions governed by the normal cone to a prox-regular set and subject to a Lipschitz perturbation. We prove that such apparently more general systems can be indeed remodeled into the classical theory of differential inclusions involving maximal monotone operators. This result permits us to make use of the rich and abundant achievements in this class of monotone operators to derive the desired existence result and stability analysis, as well as the continuity and differentiability properties of the solutions. This going back and forth between these two kinds of differential inclusions is made possible thanks to a viability result for maximal monotone operators. This is a joint work with S. Adly and Bao Tran Nguyen.