Charles Dossal
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View article: Optimization with First Order Algorithms
Optimization with First Order Algorithms Open
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze t…
View article: Gradient correlation is needed to accelerate SGD with momentum
Gradient correlation is needed to accelerate SGD with momentum Open
Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pessimistic, even in the case of convex functions, about the …
View article: Parameter-Free FISTA by Adaptive Restart and Backtracking
Parameter-Free FISTA by Adaptive Restart and Backtracking Open
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View article: Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case
Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case Open
We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show thatNAG can achieve an accelerated convergence speed at the c…
View article: Heavy Ball Momentum for Non-Strongly Convex Optimization
Heavy Ball Momentum for Non-Strongly Convex Optimization Open
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 parameter are particularly efficient (see Polyak [32], Nester…
View article: Strong Convergence of FISTA Iterates under Hölderian and Quadratic Growth Conditions
Strong Convergence of FISTA Iterates under Hölderian and Quadratic Growth Conditions Open
Introduced by Beck and Teboulle, FISTA (for Fast Iterative Shrinkage-Thresholding Algorithm) is a first-order method widely used in convex optimization. Adapted from Nesterov's accelerated gradient method for convex functions, the generate…
View article: Parameter-Free FISTA by Adaptive Restart and Backtracking
Parameter-Free FISTA by Adaptive Restart and Backtracking Open
We consider a combined restarting and adaptive backtracking strategy for the popular Fast Iterative Shrinking-Thresholding Algorithm frequently employed for accelerating the convergence speed of large-scale structured convex optimization p…
View article: A necessary and sufficient condition for exact recovery by l1 minimization.
A necessary and sufficient condition for exact recovery by l1 minimization. Open
The minimum $\\ell_1$-norm solution to an underdetermined system of linear equations $y = A x$, is often, remarkably, also the sparsest solution to that system. In this paper, we provide a \\textit{necessary} and \\textit{sufficient} condi…
View article: Geometric Estimation with Orthogonal Bandlet Bases
Geometric Estimation with Orthogonal Bandlet Bases Open
This article presents the first adaptive quasi minimax estimator for geometrically regular images in the white noise model. This estimator is computed using a thresholding in an adapted orthogonal bandlet basis optimized for the noisy obse…
View article: A greedy algorithm to extract sparsity degree for l1/l0-equivalence in a deterministic context
A greedy algorithm to extract sparsity degree for l1/l0-equivalence in a deterministic context Open
This paper investigates the problem of designing a deterministic system matrix, that is measurement matrix, for sparse recovery. An efficient greedy algorithm is proposed in order to extract the class of sparse signal/image which cannot be…
View article: Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport
Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport Open
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm)…
View article: Convergence rates of the Heavy-Ball method for quasi-strongly convex optimization
Convergence rates of the Heavy-Ball method for quasi-strongly convex optimization Open
In this paper, we study the behavior of solutions of the ODE associated to the Heavy Ball method. Since the pioneering work of B.T. Polyak [25], it is well known that such a scheme is very efficient for C2 strongly convex functions with Li…
View article: Optimal Convergence Rates for Nesterov Acceleration
Optimal Convergence Rates for Nesterov Acceleration Open
In this paper, we study the behavior of solutions of the ODE associated to Nesterov acceleration. It is well-known since the pioneering work of Nesterov that the rate of convergence $O(1/t^2)$ is optimal for the class of convex functions w…
View article: Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport Open
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp algorithm…
View article: The optimal decay for the solution of theMonotone Inclusion associated to FISTA for b<=3 is 2b/3
The optimal decay for the solution of theMonotone Inclusion associated to FISTA for b<=3 is 2b/3 Open
It was recently proved that the decay of the solution of the ODE associated to the Nesterov Fast Gradient Algorithm with a parameter b 3 was 0(1 t 2b 3). In this note we prove that this decay is achieved for the solution of the associated …
View article: Sampling the Fourier Transform Along Radial Lines
Sampling the Fourier Transform Along Radial Lines Open
This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions…
View article: Sampling the Fourier transform along radial lines
Sampling the Fourier transform along radial lines Open
This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions…