Optimization methods are at the core of many problems in signal/image processing,
computer vision, and machine learning. For a long time, it has been recognized that looking …

Deep learning (DL) has had unprecedented success and is now entering scientific
computing with full force. However, current DL methods typically suffer from instability, even …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

We revisit the proofs of convergence for a first order primal–dual algorithm for convex
optimization which we have studied a few years ago. In particular, we prove rates of …

In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization
problems with known saddle-point structure. We prove convergence to a saddle-point with …

We propose a new first-order splitting algorithm for solving jointly the primal and dual
formulations of large-scale convex minimization problems involving the sum of a smooth …

Over the last decades, the total variation (TV) has evolved to be one of the most broadly-
used regularisation functionals for inverse problems, in particular for imaging applications …

In this paper, we propose an inertial forward-backward splitting algorithm to compute a zero
of the sum of two monotone operators, with one of the two operators being co-coercive. The …

In this paper we study an algorithm for solving a minimization problem composed of a
differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The …

We consider the problem of solving dual monotone inclusions involving sums of composite
parallel-sum type operators. A feature of this work is to exploit explicitly the properties of the …