Nous présentons une analyse de la borne de complexité dans le pire des cas pour les méthodes de région de confiance en présence d'approximations du Hessien...

The purpose of the present note is to bring clarifications to certain concepts and surrounding notation of Aravkin et al. (2022). All results therein contin...

We develop a trust-region method for minimizing the sum of a smooth term \(f\) and a nonsmooth term \(h\), both of which can be nonconvex. Each iteratio...

La bibliothèque de sous-programmes Harwell (HSL) est une suite renommée de méthodes numériques efficaces et robustes conçus pour résoudre des problèmes mathé...

Improving neural network optimizer convergence speed is a long-standing priority. Recently, there has been a focus on quasi-Newton optimization methods, whi...

Historically, the training of deep artificial neural networks has relied on parallel computing to achieve practical effectiveness. However, with the increas...

We introduce an iterative solver named MINARES for symmetric linear systems \(Ax \approx b\), where \(A\) is possibly singular. MINARES is based on t...

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...