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 …
J Lee, C Park, E Ryu - Advances in Neural Information …, 2021 - proceedings.neurips.cc
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 …
C Ma, NVC Gudapati, M Jahani… - arXiv preprint arXiv …, 2017 - researchgate.net
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 …
R Tappenden, M Takáč - arXiv preprint arXiv:2211.00866, 2022 - arxiv.org
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 …