Analysis and Design of First-order Optimization Methods using the Performance Estimation Framework

Abstract:

We introduce the performance estimation (PE) approach. This methodology aims at automatically analyzing the convergence properties of first-order algorithms for solving (composite convex) optimization problems.
In particular, it allows obtaining tight guarantees for fixed-step first-order methods involving a variety of different oracles - namely explicit, projected, proximal, conditional and inexact (sub)gradient steps - and a variety of convergence measures. 

During the presentation, we will present and illustrate the PE methodology and how it can be used for developing new algorithms and convergence proofs.
(Joint works with François Glineur, Julien Hendrickx, Etienne de Klerk and Yoel Drori)