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 functionsand 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.

Posted on Oct 5, 2021 in Optimization and Equilibrium, Seminars