Numerical optimization serves as one of the pillars of machine learning. To meet the
demands of big data applications, lots of efforts have been put on designing theoretically …

First-order methods for solving convex optimization problems have been at the forefront of
mathematical optimization in the last 20 years. The rapid development of this important class …

We consider a variable metric and inexact version of the fast iterative soft-thresholding
algorithm (FISTA) type algorithm considered in [L. Calatroni and A. Chambolle, SIAM J …

Optimizing strongly convex functions subject to linear constraints is a fundamental problem
with numerous applications. In this work, we propose a block (accelerated) randomized …

We study the linear convergence of the primal-dual hybrid gradient method. After a review of
current analyses, we show that they do not explain properly the behavior of the algorithm …

We study the block-coordinate forward–backward algorithm in which the blocks are updated
in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm …

We propose a structure-adaptive variant of the state-of-the-art stochastic variance-reduced
gradient algorithm Katyusha for regularized empirical risk minimization. The proposed …

Momentum methods for convex optimization often rely on precise choices of algorithmic
parameters, based on knowledge of problem parameters, in order to achieve fast …

This paper deals with convex nonsmooth optimization problems. We introduce a general
smooth approximation framework for the original function and apply random (accelerated) …

Stochastic optimisation algorithms are the de facto standard for machine learning with large
amounts of data. Handling only a subset of available data in each optimisation step …