A block-coordinate approach of multi-level optimization with an application to physics-informed neural networks. - Gratton, Serge; Mercier, Valentin; Riccietti, Elisa; Toint, Philippe L. (Comput. Optim. Appl., 2024)

A non-linear conjugate gradient in dual space for Lp-norm regularized non-linear least squares with application in data assimilation. - Bernigaud, Antoine; Gratton, Serge; Simon, Ehouarn (Numer. Algorithms, 2024)

Preface for the special edition of optimization methods and software. - Gratton, Serge; Toint, Philippe L.; Gondzio, Jacek; Nesterov, Yurii E.; Yuan, Ya-xiang (Optim. Methods Softw., 2024)

Combining Statistical Depth and Fermat Distance for Uncertainty Quantification. - Nguyen, Hai-Vy; Gamboa, Fabrice; Chhaibi, Reda; Zhang, Sixin; Gratton, Serge; Giaccone, Thierry (2024)

Combining Statistical Depth and Fermat Distance for Uncertainty Quantification. - Nguyen, Hai-Vy; Gamboa, Fabrice; Chhaibi, Reda; Zhang, Sixin; Gratton, Serge; Giaccone, Thierry (CoRR, 2024)

Large Margin Discriminative Loss for Classification. - Nguyen, Hai-Vy; Gamboa, Fabrice; Zhang, Sixin; Chhaibi, Reda; Gratton, Serge; Giaccone, Thierry (CoRR, 2024)

CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle System. - Reverdi, Justin; Zhang, Sixin; Aoues, Saïd; Gamboa, Fabrice; Gratton, Serge; Pellegrini, Thomas (CoRR, 2024)

S2MPJ and CUTEst optimization problems for Matlab, Python and Julia. - Gratton, Serge; Toint, Philippe L. (CoRR, 2024)

Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(ε-2) rather than 𝒪(ε-2). - Gratton, Serge; Sim, Chee-Khian; Toint, Philippe L. (CoRR, 2024)

Two-level deep domain decomposition method. - Dolean, Victorita; Gratton, Serge; Heinlein, Alexander; Mercier, Valentin (CoRR, 2024)

OFFO minimization algorithms for second-order optimality and their complexity. - Gratton, Serge; Toint, Philippe L. (Comput. Optim. Appl., 2023)

An adaptive regularization method in Banach spaces. - Gratton, Serge; Jerad, Sadok; Toint, Philippe L. (Optim. Methods Softw., 2023)

Convergence Properties of an Objective-Function-Free Optimization Regularization Algorithm, Including an \(\boldsymbol{\mathcal{O}(ε^{-3/2})}\) Complexity Bound. - Gratton, Serge; Jerad, Sadok; Toint, Philippe L. (SIAM J. Optim., 2023)

Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. - Gratton, Serge; Kopanicáková, Alena; Toint, Philippe L. (SIAM J. Optim., 2023)

Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. - Gratton, Serge; Kopanicáková, Alena; Toint, Philippe L. (CoRR, 2023)

A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks. - Gratton, Serge; Mercier, Valentin; Riccietti, Elisa; Toint, Philippe L. (CoRR, 2023)

A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields. - Briant, Jérémy; Mycek, Paul; Destouches, Mayeul; Goux, Olivier; Gratton, Serge; Gürol, Selime; Simon, Ehouarn; Weaver, Anthony T. (CoRR, 2023)

On a multilevel Levenberg-Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations. - Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier (Optim. Methods Softw., 2022)

A Note on Inexact Inner Products in GMRES. - Gratton, Serge; Simon, Ehouarn; Titley-Péloquin, David; Toint, Philippe L. (SIAM J. Matrix Anal. Appl., 2022)

Parametric complexity analysis for a class of first-order Adagrad-like algorithms. - Gratton, Serge; Jerad, Sadok; Toint, Philippe L. (CoRR, 2022)

An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity. - Gratton, Serge; Simon, Ehouarn; Toint, Philippe L. (Math. Program., 2021)

Minimizing convex quadratics with variable precision conjugate gradients. - Gratton, Serge; Simon, Ehouarn; Titley-Péloquin, David; Toint, Philippe L. (Numer. Linear Algebra Appl., 2021)

On High-Order Multilevel Optimization Strategies. - Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier (SIAM J. Optim., 2021)

Latent Space Data Assimilation by using Deep Learning. - Peyron, Mathis; Fillion, Anthony; Gürol, Selime; Marchais, Victor; Gratton, Serge; Boudier, Pierre; Goret, Gaël (CoRR, 2021)

Hölder Gradient Descent and Adaptive Regularization Methods in Banach Spaces for First-Order Points. - Gratton, Serge; Jerad, Sadok; Toint, Philippe L. (CoRR, 2021)

A coarse space acceleration of deep-DDM. - Mercier, Valentin; Gratton, Serge; Boudier, Pierre (CoRR, 2021)

A note on solving nonlinear optimization problems in variable precision. - Gratton, Serge; Toint, Philippe L. (Comput. Optim. Appl., 2020)

An Iterative Ensemble Kalman Smoother in Presence of Additive Model Error. - Fillion, Anthony; Bocquet, Marc; Gratton, Serge; Gürol, Selime; Sakov, Pavel (SIAM/ASA J. Uncertain. Quantification, 2020)

A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds. - Gratton, Serge; Royer, Clément W.; Vicente, Luís Nunes (Math. Program., 2020)

On Iterative Solution of the Extended Normal Equations. - Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier (SIAM J. Matrix Anal. Appl., 2020)

DAN - An optimal Data Assimilation framework based on machine learning Recurrent Networks. - Boudier, Pierre; Fillion, Anthony; Gratton, Serge; Gürol, Selime (CoRR, 2020)

Direct search based on probabilistic feasible descent for bound and linearly constrained problems. - Gratton, Serge; Royer, Clément W.; Vicente, Luís Nunes; Zhang, Zaikun (Comput. Optim. Appl., 2019)

On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method. - Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier (CoRR, 2019)

Exploiting variable precision in GMRES. - Gratton, Serge; Simon, Ehouarn; Titley-Péloquin, David; Toint, Philippe L. (CoRR, 2019)

On the iterative solution of systems of the form ATA x=ATb+c. - Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier (CoRR, 2019)

Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening. - Lunet, Thibaut; Bodart, Julien; Gratton, Serge; Vasseur, Xavier (Comput. Vis. Sci., 2018)

A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis. - Bergou, El Houcine; Diouane, Youssef; Gratton, Serge (J. Optim. Theory Appl., 2018)

A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. - Bellavia, Stefania; Gratton, Serge; Riccietti, Elisa (Numerische Mathematik, 2018)

Low rank updates in preconditioning the saddle point systems arising from data assimilation problems. - Fisher, Matthew C.; Gratton, Serge; Gürol, Selime; Trémolet, Yannick; Vasseur, Xavier (Optim. Methods Softw., 2018)

Improved Bounds for Small-Sample Estimation. - Gratton, Serge; Titley-Péloquin, David (SIAM J. Matrix Anal. Appl., 2018)

Minimizing convex quadratic with variable precision Krylov methods. - Gratton, Serge; Simon, Ehouarn; Toint, Philippe L. (CoRR, 2018)

A note on solving nonlinear optimization problems in variable precision. - Gratton, Serge; Toint, Philippe L. (CoRR, 2018)

On the use of the energy norm in trust-region and adaptive cubic regularization subproblems. - Bergou, El Houcine; Diouane, Youssef; Gratton, Serge (Comput. Optim. Appl., 2017)

A conjugate gradient like method for p-norm minimization in functional spaces. - Estatico, Claudio; Gratton, Serge; Lenti, Flavia; Titley-Péloquin, David (Numerische Mathematik, 2017)

An indicator for the switch from derivative-free to derivative-based optimization. - Gratton, Serge; Soualmi, N.; Vicente, Luís Nunes (Oper. Res. Lett., 2017)

On the Symmetric Componentwise Relative Backward Error for Linear Systems of Equations. - Eisenstat, Stanley C.; Gratton, Serge; Titley-Péloquin, David (SIAM J. Matrix Anal. Appl., 2017)

Levenberg-Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation. - Bergou, El Houcine; Gratton, Serge; Vicente, Luís Nunes (SIAM/ASA J. Uncertain. Quantification, 2016)

Reducing complexity of algebraic multigrid by aggregation. - Gratton, Serge; Hénon, Pascal; Jiránek, Pavel; Vasseur, Xavier (Numer. Linear Algebra Appl., 2016)

On a second-order expansion of the truncated singular subspace decomposition. - Gratton, Serge; Ilunga, Jean Tshimanga (Numer. Linear Algebra Appl., 2016)

Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics. - Gratton, Serge; Mercier, Sylvain; Tardieu, Nicolas; Vasseur, Xavier (Numer. Linear Algebra Appl., 2016)

Globally convergent evolution strategies for constrained optimization. - Diouane, Youssef; Gratton, Serge; Vicente, Luís Nunes (Comput. Optim. Appl., 2015)

Observation thinning in data assimilation computations. - Gratton, Serge; Rincon-Camacho, M. Monserrat; Simon, Ehouarn; Toint, Philippe L. (EURO J. Comput. Optim., 2015)

Globally convergent evolution strategies. - Diouane, Youssef; Gratton, Serge; Vicente, Luís Nunes (Math. Program., 2015)

Quasi-Newton updates with weighted secant equations. - Gratton, Serge; Malmedy, Vincent; Toint, Philippe L. (Optim. Methods Softw., 2015)

Direct Search Based on Probabilistic Descent. - Gratton, Serge; Royer, Clément W.; Vicente, Luís Nunes; Zhang, Zaikun (SIAM J. Optim., 2015)

Conjugate gradient algorithm in Banach spaces to enhance the spatial resolution of microwave remote sensing data. - Lenti, Flavia; Estatico, Claudio; Titley-Péloquin, David; Nunziata, Ferdinando; Migliaccio, Maurizio; Gratton, Serge (2015)

Stochastic Conditioning of Matrix Functions. - Gratton, Serge; Titley-Péloquin, David (SIAM/ASA J. Uncertain. Quantification, 2014)

A surrogate management framework using rigorous trust-region steps. - Gratton, Serge; Vicente, Luís Nunes (Optim. Methods Softw., 2014)

A Merit Function Approach for Direct Search. - Gratton, Serge; Vicente, Luís Nunes (SIAM J. Optim., 2014)

Differentiating the Method of Conjugate Gradients. - Gratton, Serge; Titley-Péloquin, David; Toint, Philippe L.; Ilunga, Jean Tshimanga (SIAM J. Matrix Anal. Appl., 2014)

The Exact Condition Number of the Truncated Singular Value Solution of a Linear Ill-Posed Problem. - Bergou, El Houcine; Gratton, Serge; Ilunga, Jean Tshimanga (SIAM J. Matrix Anal. Appl., 2014)

Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. - Gratton, Serge; Gürol, Selime; Toint, Philippe L. (Comput. Optim. Appl., 2013)

An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media. - Calandra, Henri; Gratton, Serge; Pinel, Xavier; Vasseur, Xavier (Numer. Linear Algebra Appl., 2013)

Sensitivity and Conditioning of the Truncated Total Least Squares Solution. - Gratton, Serge; Titley-Péloquin, David; Ilunga, Jean Tshimanga (SIAM J. Matrix Anal. Appl., 2013)

A Modified Block Flexible GMRES Method with Deflation at Each Iteration for the Solution of Non-Hermitian Linear Systems with Multiple Right-Hand Sides. - Calandra, Henri; Gratton, Serge; Lago, Rafael; Vasseur, Xavier; Carvalho, Luiz Mariano (SIAM J. Sci. Comput., 2013)

Statistical Estimates for the Conditioning of Linear Least Squares Problems. - Baboulin, Marc; Gratton, Serge; Lacroix, Rémi; Laub, Alan J. (2013)

Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. - Gratton, Serge; Malmedy, Vincent; Toint, Philippe L. (Comput. Optim. Appl., 2012)

Linear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method. - Arioli, Mario; Gratton, Serge (Comput. Phys. Commun., 2012)

On the Accuracy of the Karlson-Waldén Estimate of the Backward Error for Linear Least Squares Problems. - Gratton, Serge; Jiránek, Pavel; Titley-Péloquin, David (SIAM J. Matrix Anal. Appl., 2012)

Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics. - Calandra, Henri; Gratton, Serge; Langou, Julien; Pinel, Xavier; Vasseur, Xavier (SIAM J. Sci. Comput., 2012)

Fast regularized linear sampling for inverse scattering problems. - Fares, M'Barek; Gratton, Serge; Toint, Philippe L. (Numer. Linear Algebra Appl., 2011)

Stopping rules and backward error analysis for bound-constrained optimization. - Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L. (Numerische Mathematik, 2011)

An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. - Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke (Optim. Methods Softw., 2011)

On A Class of Limited Memory Preconditioners For Large Scale Linear Systems With Multiple Right-Hand Sides. - Gratton, Serge; Sartenaer, Annick; Ilunga, Jean Tshimanga (SIAM J. Optim., 2011)

A Contribution to the Conditioning of the Total Least-Squares Problem. - Baboulin, Marc; Gratton, Serge (SIAM J. Matrix Anal. Appl., 2011)

Range-Space Variants and Inexact Matrix-Vector Products in Krylov Solvers for Linear Systems Arising from Inverse Problems. - Gratton, Serge; Toint, Philippe L.; Ilunga, Jean Tshimanga (SIAM J. Matrix Anal. Appl., 2011)

A Flexible Generalized Conjugate Residual Method with Inner Orthogonalization and Deflated Restarting. - Carvalho, Luiz Mariano; Gratton, Serge; Lago, Rafael; Vasseur, Xavier (SIAM J. Matrix Anal. Appl., 2011)

Variable Neighborhood Search for Robust Optimization and Applications to Aerodynamics. - Mucherino, Antonio; Fuchs, Martin; Vasseur, Xavier; Gratton, Serge (2011)

Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. - Gratton, Serge; Mouffe, Mélodie; Sartenaer, Annick; Toint, Philippe L.; Tomanos, Dimitri (Optim. Methods Softw., 2010)

Approximate invariant subspaces and quasi-newton optimization methods. - Gratton, Serge; Toint, Philippe L. (Optim. Methods Softw., 2010)

Flexible GMRES with Deflated Restarting. - Giraud, Luc; Gratton, Serge; Pinel, Xavier; Vasseur, Xavier (SIAM J. Sci. Comput., 2010)

A contribution to the conditioning of the total least squares problem - Baboulin, Marc; Gratton, Serge (CoRR, 2010)

Computing the conditioning of the components of a linear least-squares solution. - Baboulin, Marc; Dongarra, Jack J.; Gratton, Serge; Langou, Julien (Numer. Linear Algebra Appl., 2009)

Recursive Trust-Region Methods for Multiscale Nonlinear Optimization. - Gratton, Serge; Sartenaer, Annick; Toint, Philippe L. (SIAM J. Optim., 2008)

Algorithm 881: A Set of Flexible GMRES Routines for Real and Complex Arithmetics on High-Performance Computers. - Frayssé, Valérie; Giraud, Luc; Gratton, Serge (ACM Trans. Math. Softw., 2008)

A priori selection of the regularization parameters in emission tomography by Fourier synthesis. - Mariano-Goulart, Denis; Maréchal, P.; Gratton, Serge; Giraud, Luc; Fourcade, M. (Comput. Medical Imaging Graph., 2007)

A distributed packed storage for large dense parallel in-core calculations. - Baboulin, Marc; Giraud, Luc; Gratton, Serge; Langou, Julien (Concurr. Comput. Pract. Exp., 2007)

Multilevel algorithm for a Poisson noise removal model with total-variation regularization. - Duff, Iain S.; Gratton, Serge; Pinel, Xavier; Vasseur, Xavier (Int. J. Comput. Math., 2007)

Approximate Gauss-Newton Methods for Nonlinear Least Squares Problems. - Gratton, Serge; Lawless, Amos S.; Nichols, Nancy K. (SIAM J. Optim., 2007)

A Partial Condition Number for Linear Least Squares Problems. - Arioli, Mario; Baboulin, Marc; Gratton, Serge (SIAM J. Matrix Anal. Appl., 2007)

Convergence in Backward Error of Relaxed GMRES. - Giraud, Luc; Gratton, Serge; Langou, Julien (SIAM J. Sci. Comput., 2007)

Additive and Multiplicative Two-Level Spectral Preconditioning for General Linear Systems. - Carpentieri, Bruno; Giraud, Luc; Gratton, Serge (SIAM J. Sci. Comput., 2007)

A Note on GMRES Preconditioned by a Perturbed L D LT Decomposition with Static Pivoting. - Arioli, Mario; Duff, Iain S.; Gratton, Serge; Pralet, Stéphane (SIAM J. Sci. Comput., 2007)

On the Sensitivity of Some Spectral Preconditioners. - Giraud, Luc; Gratton, Serge (SIAM J. Matrix Anal. Appl., 2006)

A Parallel Distributed Solver for Large Dense Symmetric Systems: Applications to Geodesy and Electromagnetism Problems. - Baboulin, Marc; Giraud, Luc; Gratton, Serge (Int. J. High Perform. Comput. Appl., 2005)

Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers. - Frayssé, Valérie; Giraud, Luc; Gratton, Serge; Langou, Julien (ACM Trans. Math. Softw., 2005)

A Rank-k Update Procedure for Reorthogonalizing the Orthogonal Factor from Modified Gram-Schmidt. - Giraud, Luc; Gratton, Serge; Langou, Julien (SIAM J. Matrix Anal. Appl., 2004)

Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis. - Maréchal, P.; Mariano-Goulart, Denis; Giraud, Luc; Gratton, Serge (2004)

Self characterization of modelling parameters for synthetic aperture imaging radiometers. - Anterrieu, Eric; Gratton, Serge; Picard, Bruno (2003)

On the condition numbers associated with the polar factorization of a matrix. - Chaitin-Chatelin, Françoise; Gratton, Serge (Numer. Linear Algebra Appl., 2000)