On strongly quasiconvex functions (part I): existence results and generalized subdifferentials

Location: Room 612, building A6, Institute of Mathematics (18 Hoang Quoc Viet, Cau Giay, Hanoi)

Time: 9:00 - 10:00 AM, March 22nd, 2023 (Wednesday)

Abstract: 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, its applications emcompasses different problems from mathematical sciences, economics and engineering among others and especially useful for algorithms purposes. 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 study properties for the proximity operator and its applications in proximal point algorithms and we introduce a generalized subdifferential for studying nonsmooth strongly quasiconvex functions.