We introduce the performance estimation 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, links with other methodologies for automated algorithmic analysis will be emphasized, and we will illustrate how they can be used to further develop new algorithmic schemes, i.e., for obtaining better-performing (in the worst-case sense) first-order methods.