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

Gradient-based optimization algorithms can be studied from the perspective of limiting
ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not …

In a recent paper, Bubeck, Lee, and Singh introduced a new first order method for
minimizing smooth strongly convex functions. Their geometric descent algorithm, largely …

Since Nesterov's seminal 1983 work, many accelerated first-order optimization methods
have been proposed, but their analyses lacks a common unifying structure. In this work, we …

When considering the minimization of a quadratic or strongly convex function, it is well
known that first-order methods involving an inertial term weighted by a constant-in-time …

In this work we introduce the concept of an Underestimate Sequence (UES), which is a
natural extension of Nesterov's estimate sequence [16]. Our definition of a UES utilizes three …

This work shows that applying Gradient Descent (GD) with a fixed step size to minimize a
(possibly nonconvex) quadratic function is equivalent to running the Power Method (PM) on …

In this work we introduce the concept of an Underestimate Sequence (UES), which is
motivated by Nesterov's estimate sequence. Our definition of a UES utilizes three …

Ce manuscrit de thèse est consacré à l'optimisation de fonctions convexes composites dans
un cadre déterministe. Dans ce cadre, je me suis concentré sur l'analyse de convergence …

Ces trois années de thèse sont passées à une vitesse folle et c'est en grande partie grâce
aux personnes que j'ai pu cotoyer. Tant dans le cadre du travail qu'en dehors, j'ai eu la …