Abstract: In this second talk, we will continue our discussion of the performance estimation methodology and will emphasize its great versatility. We will cover many examples of tight convergence analyses that go beyond the initial setup of smooth convex optimization with fixed-step methods, focusing mainly on the results obtained in our group. These will include results about more general classes of objective functions (including nonsmooth, nonconvex and hypoconvex functions), the use of exact line-search instead of fixed step-size, the effect of inexact gradient computations, extensions to algorithms involving linear mappings (including primal-dual algorithms such as Chambolle-Pock) and block coordinate-descent algorithms. We will also highlight a few remaining open questions.

(this part is joint work with many collaborators, including Nizar Bousselmi, Etienne de Klerk, Julien M. Hendrickx, Yassine Kamri, Panos Patrinos, Teodor Rotaru and Adrien B. Taylor)