Optimal levaraging of strong convexity and smoothness for splitting algorithms

Luis M. Briceño Arias,

Universidad Técnica Federico Santa María, Santiago de Chile

Title: Optimal levaraging of strong convexity and smoothness for splitting algorithms

Abstract: In this talk, we establish a tight optimal linear convergence rates for a class of strongly convex optimization problems involving two functions, at least one of which is smooth. Our approach consists of applying the classical splitting algorithms (including proximal-gradient, FISTA, and Peaceman-Rachford algorithms) to an equivalent modified optimization problem with adjustable levels of strong convexity and smoothness. The obtained rate generalizes the known tight rates for the case in which one function is both strongly convex and smooth, and is strictly better than the best rates previously available in the general setting. The practical performance of our method is illustrated through an academic example and applications to image processing.