Serge Gratton

Publication Activity (10 Years)

Years Active: 2000-2024
Publications (10 Years): 51

Top Topics

Unconstrained Optimization

Regularization Method

Data Assimilation

Top Venues

SIAM J. Matrix Anal. Appl.

Comput. Optim. Appl.

Publications

Hai-Vy Nguyen, Fabrice Gamboa, Reda Chhaibi, Sixin Zhang, Serge Gratton, Thierry Giaccone
Combining Statistical Depth and Fermat Distance for Uncertainty Quantification. CoRR (2024)
Antoine Bernigaud, Serge Gratton, Ehouarn Simon
-norm regularized non-linear least squares with application in data assimilation. Numer. Algorithms 95 (1) (2024)
Hai-Vy Nguyen, Fabrice Gamboa, Sixin Zhang, Reda Chhaibi, Serge Gratton, Thierry Giaccone
Large Margin Discriminative Loss for Classification. CoRR (2024)
Serge Gratton, Philippe L. Toint
S2MPJ and CUTEst optimization problems for Matlab, Python and Julia. CoRR (2024)
Justin Reverdi, Sixin Zhang, Saïd Aoues, Fabrice Gamboa, Serge Gratton, Thomas Pellegrini
CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle System. CoRR (2024)
Serge Gratton, Sadok Jerad, Philippe L. Toint
An adaptive regularization method in Banach spaces. Optim. Methods Softw. 38 (6) (2023)
Jérémy Briant, Paul Mycek, Mayeul Destouches, Olivier Goux, Serge Gratton, Selime Gürol, Ehouarn Simon, Anthony T. Weaver
A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields. CoRR (2023)
Serge Gratton, Philippe L. Toint
OFFO minimization algorithms for second-order optimality and their complexity. Comput. Optim. Appl. 84 (2) (2023)
Serge Gratton, Alena Kopanicáková, Philippe L. Toint
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. SIAM J. Optim. 33 (4) (2023)
Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L. Toint
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks. CoRR (2023)
Serge Gratton, Sadok Jerad, Philippe L. Toint
Convergence Properties of an Objective-Function-Free Optimization Regularization Algorithm, Including an \(\boldsymbol{\mathcal{O}(\epsilon^{-3/2})}\) Complexity Bound. SIAM J. Optim. 33 (3) (2023)
Serge Gratton, Alena Kopanicakova, Philippe L. Toint
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. CoRR (2023)
Serge Gratton, Ehouarn Simon, David Titley-Péloquin, Philippe L. Toint
A Note on Inexact Inner Products in GMRES. SIAM J. Matrix Anal. Appl. 43 (3) (2022)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On a multilevel Levenberg-Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations. Optim. Methods Softw. 37 (1) (2022)
Serge Gratton, Sadok Jerad, Philippe L. Toint
Parametric complexity analysis for a class of first-order Adagrad-like algorithms. CoRR (2022)
Valentin Mercier, Serge Gratton, Pierre Boudier
A coarse space acceleration of deep-DDM. CoRR (2021)
Serge Gratton, Ehouarn Simon, David Titley-Péloquin, Philippe L. Toint
Minimizing convex quadratics with variable precision conjugate gradients. Numer. Linear Algebra Appl. 28 (1) (2021)
Mathis Peyron, Anthony Fillion, Selime Gürol, Victor Marchais, Serge Gratton, Pierre Boudier, Gaël Goret
Latent Space Data Assimilation by using Deep Learning. CoRR (2021)
Serge Gratton, Ehouarn Simon, Philippe L. Toint
An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity. Math. Program. 187 (1) (2021)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On High-Order Multilevel Optimization Strategies. SIAM J. Optim. 31 (1) (2021)
Serge Gratton, Sadok Jerad, Philippe L. Toint
Hölder Gradient Descent and Adaptive Regularization Methods in Banach Spaces for First-Order Points. CoRR (2021)
Pierre Boudier, Anthony Fillion, Serge Gratton, Selime Gürol
DAN - An optimal Data Assimilation framework based on machine learning Recurrent Networks. CoRR (2020)
Serge Gratton, Philippe L. Toint
A note on solving nonlinear optimization problems in variable precision. Comput. Optim. Appl. 76 (3) (2020)
Serge Gratton, Clément W. Royer, Luís Nunes Vicente
A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds. Math. Program. 179 (1) (2020)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On Iterative Solution of the Extended Normal Equations. SIAM J. Matrix Anal. Appl. 41 (4) (2020)
Anthony Fillion, Marc Bocquet, Serge Gratton, Selime Gürol, Pavel Sakov
An Iterative Ensemble Kalman Smoother in Presence of Additive Model Error. SIAM/ASA J. Uncertain. Quantification 8 (1) (2020)
Serge Gratton, Ehouarn Simon, David Titley-Péloquin, Philippe L. Toint
Exploiting variable precision in GMRES. CoRR (2019)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method. CoRR (2019)
Serge Gratton, Clément W. Royer, Luís Nunes Vicente, Zaikun Zhang
Direct search based on probabilistic feasible descent for bound and linearly constrained problems. Comput. Optim. Appl. 72 (3) (2019)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
b+c. CoRR (2019)
El Houcine Bergou, Youssef Diouane, Serge Gratton
A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis. J. Optim. Theory Appl. 178 (3) (2018)
Thibaut Lunet, Julien Bodart, Serge Gratton, Xavier Vasseur
Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening. Comput. Vis. Sci. 19 (1-2) (2018)
Serge Gratton, David Titley-Péloquin
Improved Bounds for Small-Sample Estimation. SIAM J. Matrix Anal. Appl. 39 (2) (2018)
Matthew C. Fisher, Serge Gratton, Selime Gürol, Yannick Trémolet, Xavier Vasseur
Low rank updates in preconditioning the saddle point systems arising from data assimilation problems. Optim. Methods Softw. 33 (1) (2018)
Serge Gratton, Philippe L. Toint
A note on solving nonlinear optimization problems in variable precision. CoRR (2018)
Stefania Bellavia, Serge Gratton, Elisa Riccietti
A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. Numerische Mathematik 140 (3) (2018)
Serge Gratton, Ehouarn Simon, Philippe L. Toint
Minimizing convex quadratic with variable precision Krylov methods. CoRR (2018)
Claudio Estatico, Serge Gratton, Flavia Lenti, David Titley-Péloquin
A conjugate gradient like method for p-norm minimization in functional spaces. Numerische Mathematik 137 (4) (2017)
El Houcine Bergou, Youssef Diouane, Serge Gratton
On the use of the energy norm in trust-region and adaptive cubic regularization subproblems. Comput. Optim. Appl. 68 (3) (2017)
Stanley C. Eisenstat, Serge Gratton, David Titley-Péloquin
On the Symmetric Componentwise Relative Backward Error for Linear Systems of Equations. SIAM J. Matrix Anal. Appl. 38 (4) (2017)
Serge Gratton, N. Soualmi, Luís Nunes Vicente
An indicator for the switch from derivative-free to derivative-based optimization. Oper. Res. Lett. 45 (4) (2017)
El Houcine Bergou, Serge Gratton, Luís Nunes Vicente
Levenberg-Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation. SIAM/ASA J. Uncertain. Quantification 4 (1) (2016)
Serge Gratton, Pascal Hénon, Pavel Jiránek, Xavier Vasseur
Reducing complexity of algebraic multigrid by aggregation. Numer. Linear Algebra Appl. 23 (3) (2016)
Serge Gratton, Sylvain Mercier, Nicolas Tardieu, Xavier Vasseur
Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics. Numer. Linear Algebra Appl. 23 (5) (2016)
Serge Gratton, Jean Tshimanga Ilunga
On a second-order expansion of the truncated singular subspace decomposition. Numer. Linear Algebra Appl. 23 (3) (2016)
Flavia Lenti, Claudio Estatico, David Titley-Péloquin, Ferdinando Nunziata, Maurizio Migliaccio, Serge Gratton
Conjugate gradient algorithm in Banach spaces to enhance the spatial resolution of microwave remote sensing data. IGARSS (2015)
Serge Gratton, M. Monserrat Rincon-Camacho, Ehouarn Simon, Philippe L. Toint
Observation thinning in data assimilation computations. EURO J. Comput. Optim. 3 (1) (2015)
Serge Gratton, Clément W. Royer, Luís Nunes Vicente, Zaikun Zhang
Direct Search Based on Probabilistic Descent. SIAM J. Optim. 25 (3) (2015)
Serge Gratton, Vincent Malmedy, Philippe L. Toint
Quasi-Newton updates with weighted secant equations. Optim. Methods Softw. 30 (4) (2015)
Youssef Diouane, Serge Gratton, Luís Nunes Vicente
Globally convergent evolution strategies. Math. Program. 152 (1-2) (2015)
Youssef Diouane, Serge Gratton, Luís Nunes Vicente
Globally convergent evolution strategies for constrained optimization. Comput. Optim. Appl. 62 (2) (2015)
Serge Gratton, Luís Nunes Vicente
A surrogate management framework using rigorous trust-region steps. Optim. Methods Softw. 29 (1) (2014)
Serge Gratton, Luís Nunes Vicente
A Merit Function Approach for Direct Search. SIAM J. Optim. 24 (4) (2014)
Serge Gratton, David Titley-Péloquin, Philippe L. Toint, Jean Tshimanga Ilunga
Differentiating the Method of Conjugate Gradients. SIAM J. Matrix Anal. Appl. 35 (1) (2014)
Serge Gratton, David Titley-Péloquin
Stochastic Conditioning of Matrix Functions. SIAM/ASA J. Uncertain. Quantification 2 (1) (2014)
El Houcine Bergou, Serge Gratton, Jean Tshimanga Ilunga
The Exact Condition Number of the Truncated Singular Value Solution of a Linear Ill-Posed Problem. SIAM J. Matrix Anal. Appl. 35 (3) (2014)
Henri Calandra, Serge Gratton, Rafael Lago, Xavier Vasseur, Luiz Mariano Carvalho
A Modified Block Flexible GMRES Method with Deflation at Each Iteration for the Solution of Non-Hermitian Linear Systems with Multiple Right-Hand Sides. SIAM J. Sci. Comput. 35 (5) (2013)
Serge Gratton, Selime Gürol, Philippe L. Toint
Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. Comput. Optim. Appl. 54 (1) (2013)
Marc Baboulin, Serge Gratton, Rémi Lacroix, Alan J. Laub
Statistical Estimates for the Conditioning of Linear Least Squares Problems. PPAM (1) (2013)
Henri Calandra, Serge Gratton, Xavier Pinel, Xavier Vasseur
An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media. Numer. Linear Algebra Appl. 20 (4) (2013)
Serge Gratton, David Titley-Péloquin, Jean Tshimanga Ilunga
Sensitivity and Conditioning of the Truncated Total Least Squares Solution. SIAM J. Matrix Anal. Appl. 34 (3) (2013)
Mario Arioli, Serge Gratton
Linear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method. Comput. Phys. Commun. 183 (11) (2012)
Henri Calandra, Serge Gratton, Julien Langou, Xavier Pinel, Xavier Vasseur
Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics. SIAM J. Sci. Comput. 34 (2) (2012)
Serge Gratton, Pavel Jiránek, David Titley-Péloquin
On the Accuracy of the Karlson-Waldén Estimate of the Backward Error for Linear Least Squares Problems. SIAM J. Matrix Anal. Appl. 33 (3) (2012)
Serge Gratton, Vincent Malmedy, Philippe L. Toint
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Comput. Optim. Appl. 51 (3) (2012)
Antonio Mucherino, Martin Fuchs, Xavier Vasseur, Serge Gratton
Variable Neighborhood Search for Robust Optimization and Applications to Aerodynamics. LSSC (2011)
Serge Gratton, Philippe L. Toint, Jean Tshimanga Ilunga
Range-Space Variants and Inexact Matrix-Vector Products in Krylov Solvers for Linear Systems Arising from Inverse Problems. SIAM J. Matrix Anal. Appl. 32 (3) (2011)
Marc Baboulin, Serge Gratton
A Contribution to the Conditioning of the Total Least-Squares Problem. SIAM J. Matrix Anal. Appl. 32 (3) (2011)
Luiz Mariano Carvalho, Serge Gratton, Rafael Lago, Xavier Vasseur
A Flexible Generalized Conjugate Residual Method with Inner Orthogonalization and Deflated Restarting. SIAM J. Matrix Anal. Appl. 32 (4) (2011)
M'Barek Fares, Serge Gratton, Philippe L. Toint
Fast regularized linear sampling for inverse scattering problems. Numer. Linear Algebra Appl. 18 (1) (2011)
Serge Gratton, Annick Sartenaer, Jean Tshimanga Ilunga
On A Class of Limited Memory Preconditioners For Large Scale Linear Systems With Multiple Right-Hand Sides. SIAM J. Optim. 21 (3) (2011)
Serge Gratton, Philippe L. Toint, Anke Tröltzsch
An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Optim. Methods Softw. 26 (4-5) (2011)
Serge Gratton, Mélodie Mouffe, Philippe L. Toint
Stopping rules and backward error analysis for bound-constrained optimization. Numerische Mathematik 119 (1) (2011)
Serge Gratton, Mélodie Mouffe, Annick Sartenaer, Philippe L. Toint, Dimitri Tomanos
Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Optim. Methods Softw. 25 (3) (2010)
Marc Baboulin, Serge Gratton
A contribution to the conditioning of the total least squares problem CoRR (2010)
Luc Giraud, Serge Gratton, Xavier Pinel, Xavier Vasseur
Flexible GMRES with Deflated Restarting. SIAM J. Sci. Comput. 32 (4) (2010)
Serge Gratton, Philippe L. Toint
Approximate invariant subspaces and quasi-newton optimization methods. Optim. Methods Softw. 25 (4) (2010)
Marc Baboulin, Jack J. Dongarra, Serge Gratton, Julien Langou
Computing the conditioning of the components of a linear least-squares solution. Numer. Linear Algebra Appl. 16 (7) (2009)
Serge Gratton, Annick Sartenaer, Philippe L. Toint
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization. SIAM J. Optim. 19 (1) (2008)
Valérie Frayssé, Luc Giraud, Serge Gratton
Algorithm 881: A Set of Flexible GMRES Routines for Real and Complex Arithmetics on High-Performance Computers. ACM Trans. Math. Softw. 35 (2) (2008)
Mario Arioli, Marc Baboulin, Serge Gratton
A Partial Condition Number for Linear Least Squares Problems. SIAM J. Matrix Anal. Appl. 29 (2) (2007)
Luc Giraud, Serge Gratton, Julien Langou
Convergence in Backward Error of Relaxed GMRES. SIAM J. Sci. Comput. 29 (2) (2007)
Bruno Carpentieri, Luc Giraud, Serge Gratton
Additive and Multiplicative Two-Level Spectral Preconditioning for General Linear Systems. SIAM J. Sci. Comput. 29 (4) (2007)
Mario Arioli, Iain S. Duff, Serge Gratton, Stéphane Pralet
Decomposition with Static Pivoting. SIAM J. Sci. Comput. 29 (5) (2007)
Serge Gratton, Amos S. Lawless, Nancy K. Nichols
Approximate Gauss-Newton Methods for Nonlinear Least Squares Problems. SIAM J. Optim. 18 (1) (2007)
Iain S. Duff, Serge Gratton, Xavier Pinel, Xavier Vasseur
Multilevel algorithm for a Poisson noise removal model with total-variation regularization. Int. J. Comput. Math. 84 (8) (2007)
Denis Mariano-Goulart, P. Maréchal, Serge Gratton, Luc Giraud, M. Fourcade
A priori selection of the regularization parameters in emission tomography by Fourier synthesis. Comput. Medical Imaging Graph. 31 (7) (2007)
Marc Baboulin, Luc Giraud, Serge Gratton, Julien Langou
A distributed packed storage for large dense parallel in-core calculations. Concurr. Comput. Pract. Exp. 19 (4) (2007)
Luc Giraud, Serge Gratton
On the Sensitivity of Some Spectral Preconditioners. SIAM J. Matrix Anal. Appl. 27 (4) (2006)
Valérie Frayssé, Luc Giraud, Serge Gratton, Julien Langou
Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers. ACM Trans. Math. Softw. 31 (2) (2005)
Marc Baboulin, Luc Giraud, Serge Gratton
A Parallel Distributed Solver for Large Dense Symmetric Systems: Applications to Geodesy and Electromagnetism Problems. Int. J. High Perform. Comput. Appl. 19 (4) (2005)
P. Maréchal, Denis Mariano-Goulart, Luc Giraud, Serge Gratton
Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis. ECCV Workshops CVAMIA and MMBIA (2004)
Luc Giraud, Serge Gratton, Julien Langou
Update Procedure for Reorthogonalizing the Orthogonal Factor from Modified Gram-Schmidt. SIAM J. Matrix Anal. Appl. 25 (4) (2004)
Eric Anterrieu, Serge Gratton, Bruno Picard
Self characterization of modelling parameters for synthetic aperture imaging radiometers. IGARSS (2003)
Françoise Chaitin-Chatelin, Serge Gratton
On the condition numbers associated with the polar factorization of a matrix. Numer. Linear Algebra Appl. 7 (5) (2000)