JSOSuite.jl est un nouveau package Julia offrant une interface conviviale pour l'optimisation non linéaire continue. Les solveurs disponibles sont ceux de l'...

Nous étendons les analyses de complexité traditionnelles des méthodes de régions de confiance pour l'optimisation sans contrainte, possiblement non convexe....

Nous présentons RipQP, un algorithme de points intérieurs pour l'optimisation quadratique convexe écrit en Julia, libre de droit, dont le code source est lib...

Les méthodes de lagrangien augmenté (AL) forment une classe bien connue d’algorithmes pour les problèmes d’optimisation sous contraintes. Elles ont été é...

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...

Nous développons une méthode de points intérieurs pour l'optimisation non lisse régularisée avec contraintes de bornes. Notre méthode résout de manière ité...

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...

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 ...

Dans ce papier, nous comparons la méthode BFGS à la méthode du gradient conjugué (CG) pour résoudre un problème d'optimisation sans contrainte avec un algori...

Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where t...

Suite aux travaux de Estrin et al. (2019), nous développons une méthode pour l’optimisation avec contraintes générales basée sur une fonction de pénalité d...

La méthode des résidus minimaux (MINRES) de Paige et Saunders (1975), qui est souvent la méthode privilégiée pour les systèmes linéaires symétriques, est une...

Nous proposons une méthode itérative pour la résolution de systèmes de point de selle symétriques qui exploite la tridiagonalisation orthogonale de Saunders,...

Nous proposons une méthode de régularisation pour les problèmes aux moindres carrés non linéaires avec contraintes d'égalité. Notre appliquons les approches...

Nous proposons un algorithm pour les problèmes d’optimisation non linéaire avec contraintes d’égalité basé sur une fonction de pénalité lisse proposée par ...

We describe LNLQ for solving the least-norm problem \(\min\ \|x\|\) subject to \(Ax=b\). Craig's method is known to be equivalent to applying the conjug...

We propose an infeasible interior-point algorithm for constrained linear least-squares problems based on the primal-dual regularization of convex program...

Dans cet article, nous proposons une méthode d'optimisation sans factorisation pour les problèmes avec contraintes d'égalité pour lequel toutes les contrai...

For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly-constrained (LCL) augmented-La...

Nous considérons les problèmes d'optimisation sans dérivées avec variables continues, entières, discrètes et de catégorie dans le contexte d'applications i...

We study X-ray tomograqphic reconstruction using statistical methods. The problem is expressed in cylindrical coordinates, which yield significant computatio...

La Programmation Dynamique Stochastique (PDS) est une puissante méthode applicable aux problèmes mutli-étapes non-convexes et stochastiques. Nous étudions ...

Nous proposons une méthode itérative pour les problèmes aux moindres carrés linéaires \(A x \approx b\) nommée LSLQ. La méthode repose sur le processus ...

La quadrature de Gauss-Radau nous permet d'obtenir une borne supérieure peu coûteuse sur l'erreur en norme Euclidienne associée aux itérés de SYMMLQ appliqu...

NLP.py constitue un écosystème de programmation simplifiant le développement d'algorithmes d'optimisation dans un langage de haut-niveau aussi puissant ...

Une collection de systèmes linéaires engendrés au cours des itérations d'une méthode de points intérieurs pour l'optimisation quadratique convexe est...

Adaptative cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems with a shifted Hessian in the spirit of the mo...

Dans de nombreuses applications réelles d'ingénierie, il est impossible de stocker les Jacobiens ou les Hessiens de manière explicite. L'implémentation de mé...

A preconditioned variant of the Golub and Kahan (1965) bidiagonalization process recently proposed by Arioli (2013) and Arioli and Orban (2013) allows us to ...

We propose a generalization of the limited-memory Cholesky factorization of Lin and Moré (1999) to the symmetric indefinite case with special interest in sym...

Symmetric quasi-definite systems may be interpreted as regularized linear least-squares problem in appropriate metrics and arise from applications such as re...

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CU...

Projected Krylov methods are full-space formulations of Krylov methods that take place in a nullspace. Provided projections into the nullspace can be compute...

Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequ...

Interior-point methods in semi-definite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions...

OPAL is a general-purpose system for modeling and solving algorithm optimization problems. OPAL takes an algorithm as input, and as output it suggests para...

Implementations of the Simplex method differ only in very specific aspects such as the pivot rule. Similarly, most relaxation methods for mixed-integer ...

The analytic center cutting plane method and its proximal variant are well known techniques for solving convex programming problems. We propose two seq...

We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nonde...

We propose an interior-point algorithm based on an elastic formulation of the \(\ell_1\)-penalty merit function for mathematical programs with complementar...

Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear ...

Parameterizing source code for architecture-bound optimization is a common approach to high-performance programming but one that makes the programmer's task ...

We propose a modified primal-dual interior-point method for nonlinear programming that relaxes the requirement of closely following the central path and lend...

In the context of algorithmic parameter optimization, there is much room for efficient usage of computational resources. We consider the OPAL framework in wh...

A mixed interior/exterior-point method for nonlinear programming is described, that handles constraints by way of an <i>l</i>₁-penalty function. A...

We introduce the OPAL framework in which the identification of good algorithmic parameters is interpreted as a black box optimization problem whose variables...

This intentionally short tutorial is an introduction to the main features of AMPL that are relevant to nonlinear optimization model authoring. Pointers are g...

The Improved Primal Simplex algorithm IPS [8] is a dynamic constraint reduction method particularly effective on degenerate linear programs. It is able to ac...

We present a procedure for self calibration of a pinhole camera subject to radial distortion. Radial distortion parameters are estimated using a nonlinear le...

We propose a class of projected Krylov methods for the solution of unsymmetric augmented systems of equations such as those arising from the finite-element f...

We describe LANCELOT_simple, an interface to the LANCELOT B nonlinear optimization package within the GALAHAD library (Gould, Orban and Toint, 2003) which ig...

In this paper, we examine sets of tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence ...

We recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in ...

Optimization problems modeled in the AMPL modeling language [Fourer, Gay and Kernighan (2002)] may be examined by a set of tools found in the AMPL Library [...

We propose a unified framework for the update of the barrier parameter in interiorpoint methods for nonlinear programming. The original primal-dual system i...

The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algo...

In this paper, we examine the sensitivity of trust-region algorithms on the param- eters related to the step acceptance and update of the trust region. We s...

Recent developments in numerical methods for solving large differentiable nonlinear optimization problems are reviewed. State-of-the-art algorithms for solv...