This dissertation presents a novel convolutional dictionary learning algorithm for signals with a large number of channels. This algorithm uses low-rank updates for the dictionary, so that a matrix decomposition necessary for pursuit can be updated efficiently. In later chapters, this algorithm is applied to multi-layer dictionary models with multi...
In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors' previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In particular this allows one to compute some gradients, proximal terms, and/or linear minimization oracles in an ine...
In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(µ/µw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the A...
We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimization problem is the sum of the local convex costs of...
In this thesis we propose some variational methods for the mathematical and numerical analysis of a class of HJ equations. Thanks to the metric character of these equations, the set of subsolution corresponds to the set of 1-Lipschitz functions with respect to the Finsler metric associated to the Hamiltonian. Equivalently, it corresponds to the set...
Handling stress constraints is an important topic in topology optimization. In this paper, we introduce an interpretation of stresses as optimization variables, leading to an augmented Lagrangian formulation. This formulation takes two sets of optimization variables, i.e., an auxiliary stress variable per element, in addition to a density variable ...
An approximate first order quasilinear hyperbolic model for Euler-Korteweg (E-K) equations, describing compressible fluid flows whose energy depend on the gradient of density, is derived. E-K system can be seen as the Euler-Lagrange equations to a Lagrangian submitted to the mass conservation constraint. Due to the presence of the density gradient ...
Published in Magnetic resonance in medicine
Purpose: Quantitative susceptibility mapping is usually performed by minimizing a functional with data fidelity and regularization terms. A weighting parameter controls the balance between these terms. There is a need for techniques to find the proper balance that avoids artifact propagation and loss of details. Finding the point of maximum curvatu...
The presented work is dedicated to the mathematical and numerical modeling of unsteady single-and two-phase flows using finite volume and penalty methods. Two classes of Navier-Stokes solvers are considered in order to compare their accuracy and robustness, as well as to highlight their limitations. Exact (or monolythic) solvers such as the Augment...
Published in Journal of Scientific Computing
In this paper, we propose a new class of imaging denoising models by using the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-norm of mean curvat...
