We introduce a variant of the proximal gradient method in which the quadratic term is diagonal but may be indefinite, and is safeguarded by a trust region. ...

We present a Julia framework dedicated to partially-separable problems whose element function are detected automatically. This framework takes advantage of ...

Cet article présente \(\texttt{Krylov.jl}\), un module Julia qui contient une collection de processus et méthodes de Krylov pour résoudre une variété de pr...

We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squares term \(f(x) = \tfrac{1}{2} \|F(x)\|_2^2\) and a nonsmoo...

This paper presents PDENLPModels.jl a new Julia package for modeling and discretizing optimization problems with mixed algebraic and partial differential equ...

Nous considérons la méthode de surrelaxation successive généralisée (GSOR) pour la résolution d’une classe de systèmes de points de selle à trois par trois...

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is ...

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous sem...

Nous proposons une procédure pour calculer une projection de \(w \in ℝ^n\) dans l'intersection de la soi-disant boule en norme zéro \(k B_0\) de rayon ...

This paper presents DCISolver.jl a new Julia package implementating the Dynamic Control of Infeasibility method (DCI), introduced by Bielschowsky & Gomes (20...

We introduce an iterative method named GPMR for solving 2X2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously...

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-orde...

We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed...

L'algorithme NCL est conçu pour les problèmes d'optimisation lisse dont les dérivées premières et secondes sont disponibles, y compris les problèmes dont ...

We propose a new stochastic variance-reduced damped L-BFGS algorithm, where we leverage estimates of bounds on the largest and smallest eigenvalues of the He...

We present a modeling of bundle adjustment problems in Julia, as well as a solver for non-linear least square problems (including bundle adjustment problems)...

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate sub...

Nous développons des bornes sur les valeurs propres d’une nouvelle formulation des équations de Newton dans les méthodes de points intérieurs pour l’optimisa...

Artificial Intelligence (AI) is the next society transformation builder. Massive AI-based applications include cloud servers, cell phones, cars, and pandemic...

We introduce an iterative method named BiLQ for solving general square linear systems \(Ax=b\) based on the Lanczos biorthogonalization process defined by ...