The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Poljak in 1966. It is the natural extension of the class of the strongly convex functions and their applications emcompasses different problems from mathematical sciences, economics and engineering among others. In this talk, we present an overview on strongly quasiconvex functions from the open question regarding the existence of solutions for the minimization problem formulated by Poljak in 1966 until its solution in 2022. As a consequence, we present two applications in continuous optimization; An study of the proximity operator and its applications in proximal point algorithms and a generalized subdifferential for studying nonsmooth strongly quasiconvex functions and its applications in subgradient methods.
Apoiadores / Parceiros / Patrocinadores
Felipe Lara is an Assistant Professor at Departamento de Matemática in the University of Tarapacá in Arica, Chile. He obtained his Ph.D. degree in 2015 on continuous optimization in the University of Concepción. He was a postdoctoral researcher in University of Tarapacá (2015-2017) in Chile, and in the Instituto de Matemática Pura e Aplicada IMPA (2017-2018) and in the Getulio Vargas Foundation (2018-2019), both in Rio de Janeiro, Brazil. His research interests are on nonconvex nonsmooth optimization problems, from existence of solutions and optimality conditions to iterative algorithms.