Resumo

During the last decade many efforts have been made to develop continuous and discrete time approaches to nonsmooth nonconvex optimization problems, in many cases by relying on tools and techniques used in solution methods for convex optimization problems. In this talk we will review such approaches designed to solve nonsmooth nonconvex optimization problems with various structural complexities. We will discuss the pillars of the asymptotic/convergence analysis and also emphasize the role played by the Kurdyka-Lojasiewicz property in proving global convergence and in deriving convergence rates. The talk is based on joint works with H. Attouch, S. Banert, E.R. Csetnek, S. László and D.-K. Nguyen.