Performance estimation toolbox (PESTO): Automated worst-case analysis of first-order optimization methods

Abstract

We present a Matlab toolbox that automatically computes tight worst-case performance guarantees for a broad class of first-order methods for convex optimization. The class of methods includes those performing explicit, projected, proximal, conditional and inexact (sub)gradient steps. The toolbox relies on the performance estimation (PE) framework, which recently emerged through works of Drori and Teboulle and the authors. The PE approach is a very systematic manner of obtaining non-improvable worst-case guarantees for first-order numerical optimization schemes. However, using the PE methodology requires modelling efforts from the user, along with some knowledge of semidefinite programming. The goal of this work is to ease the use of the performance estimation methodology, by providing a toolbox that implicitly does the modelling job. In short, its aim is to (i) let the user write the algorithm in a natural way, as he/she would have implemented it, and (ii) let the computer perform the modelling and worst-case analysis parts automatically.