This monograph covers some recent advances in a range of acceleration techniques
frequently used in convex optimization. We first use quadratic optimization problems to …

This work establishes new convergence guarantees for gradient descent in smooth convex
optimization via a computer-assisted analysis technique. Our theory allows nonconstant …

PEPit is a python package aiming at simplifying the access to worst-case analyses of a large
family of first-order optimization methods possibly involving gradient, projection, proximal, or …

The differential equation (DE) approach for convex optimization, which relates optimization
methods to specific continuous DEs with rate-revealing Lyapunov functionals, has gained …

We propose a methodology for studying the performance of common splitting methods
through semidefinite programming. We prove tightness of the methodology and demonstrate …

We propose the first global accelerated gradient method for Riemannian manifolds. Toward
establishing our results, we revisit Nesterov's estimate sequence technique and develop a …

We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a
unified methodology for constructing optimal first-order methods for convex and nonconvex …

First-order methods are often analyzed via their continuous-time models, where their worst-
case convergence properties are usually approached via Lyapunov functions. In this work …

We propose a novel methodology that systematically analyzes ordinary differential equation
(ODE) models for first-order optimization methods by converting the task of proving …

We provide a novel computer-assisted technique for systematically analyzing first-order
methods for optimization. In contrast with previous works, the approach is particularly suited …