On strongly quasiconvex functions: theory and applications

Speaker: Profesor  Felipe Lara Obreque

Department of Mathematics, University of Tarapacá, Arica, Chile

Date:  October 06,  2021 at 10:00 am (Chilean-time)

Title:   On strongly quasiconvex functions: theory and applications

Abstract:  In this talk, we present a new existence result for the classof  lsc strongly quasiconvex functions by showing that every strongly  quasiconvex function is 2-supercoercive (in particular, coercive).  Furthermore, we investigate the usual properties of proximal operators  for strongly quasiconvex functions. In particular, we prove that the set of  fixed points of the proximal operator coincides with the unique  minimizer of a lsc strongly quasiconvex function. As a consequence, we implemented the proximal point algorithm for finding the unique solution of the  minimization problem by using a positive sequence of parameters bounded away from 0 and, in particular, we revisited the general quasiconvex case.  Moreover, a new subdifferential for nonconvex functions and a new characterization for convex functions is derived from our study. Finally, an application for a strongly quasiconvex function which is neither convex  nor differentiable nor locally Lipschitz continuous, is provided.

Venue: Online via Google Meet: https://meet.google.com/vpx-itqq-oik

A brief biography of the speaker: Felipe Lara is assistant professor at the Department of Mathematics, University of Tarapacá, Arica, Chile. He obtained his Ph.D. degree at the University of Concepción in 2015. His research interests are in continuous optimization, especially in nonconvex nonsmooth optimization.

Coordinators: Fabián Flores-Bazán (CMM, Universidad de Concepción) and Abderrahim Hantoute (Alicante)