Dominique Orban

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The Harwell Subroutine Library (HSL) is a renowned suite of efficient and robust numerical algorithms designed to tackle complex mathematical problems such a...

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We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of Ar...

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

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

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

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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. ...

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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...

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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...

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

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This paper presents \(\texttt{Krylov.jl}\), a Julia package that implements a collection of Krylov processes and methods for solving a variety of linear pr...

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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...

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

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We consider the generalized successive overrelaxation (GSOR) method for solving a class of block three-by-three saddle-point problems. Based on the necessary...

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

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

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We describe a procedure to compute a projection of \(w \in ℝ^n\) into the intersection of the so-called zero-norm ball \(k B_0\) of radius \(k\), i....

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

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

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

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

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