On strongly quasiconvex functions (part II): proximal point algorithms and open problems

Time: 9:00 - 10:00 AM, Date: March 29th, 2023 (Wednesday)

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

Abstract: In this talk, we study the convergence of the proximal point algorithm (PPA henceforth) for the minimization problem of strongly quasiconvex functions and its accelerations as the inertial-relaxed versions as well as its generalization for Bregman distances. Furthermore, we extend this analysis to pseudomonotone equilibrium problems. Moreover, and using the study of the subgradient projection method with the strong subdifferential, we present two extragradient methods for dealing with pseudomonotone equilibrium problems. Finally, we present two open problems; connections between generalized convexity and generalized monotonicity and optimality conditions for the sum of two functions in which one of them is nonsmooth and strongly quasiconvex.