Title<\/strong>:\u00a0\u00a0 On strongly quasiconvex functions: theory and applications<\/p>\n Abstract:\u00a0 <\/b>In this talk, we present a new existence result for the classof\u00a0 lsc strongly quasiconvex functions by showing that every strongly\u00a0 quasiconvex function is 2-supercoercive (in particular, coercive).\u00a0 Furthermore, we investigate the usual properties of proximal operators\u00a0 for strongly quasiconvex functions. In particular, we prove that the set of\u00a0 fixed points of the proximal operator coincides with the unique\u00a0 minimizer of a lsc strongly quasiconvex function. As a consequence, we implemented the proximal point algorithm for finding the unique solution of the\u00a0 minimization problem by using a positive sequence of parameters bounded away from 0 and, in particular, we revisited the general quasiconvex case.\u00a0 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\u00a0 nor differentiable nor locally Lipschitz continuous, is provided.<\/p>\n Venue<\/strong>: Online via Google Meet: https:\/\/meet.google.com\/vpx-itqq-oik<\/span><\/p>\n <\/span><\/span>A brief biography of the speaker<\/span><\/span><\/strong>: Felipe Lara is assistant professor at the Department of Mathematics, University of Tarapac\u00e1, Arica, Chile. He obtained his Ph.D. degree at the University of Concepci\u00f3n in 2015. His research interests are in continuous optimization, especially in nonconvex nonsmooth optimization.<\/span><\/p>\n Coordinators<\/strong>: Fabi\u00e1n Flores-Baz\u00e1n (CMM, Universidad de Concepci\u00f3n) and Abderrahim Hantoute (Alicante)<\/p>\n","protected":false},"excerpt":{"rendered":" Speaker: Profesor\u00a0 Felipe Lara Obreque Department of Mathematics, University of Tarapac\u00e1, Arica, Chile Date:\u00a0 October 06,\u00a0 2021 at 10:00 am (Chilean-time) Title:\u00a0\u00a0 On strongly quasiconvex functions: theory and applications Abstract:\u00a0 In this talk, we present a new existence result for the classof\u00a0 lsc strongly quasiconvex functions by showing that every strongly\u00a0 quasiconvex function is 2-supercoercive … Continue reading On strongly quasiconvex functions: theory and applications<\/span>