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2020 – today
- 2024
[j74]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. Comput. Optim. Appl. 89(2): 385-417 (2024)- [j73]Antoine Bernigaud, Serge Gratton, Ehouarn Simon:
A non-linear conjugate gradient in dual space for Lp-norm regularized non-linear least squares with application in data assimilation. Numer. Algorithms 95(1): 471-497 (2024) - [j72]Serge Gratton, Philippe L. Toint, Jacek Gondzio, Yurii E. Nesterov, Ya-xiang Yuan:
Preface for the special edition of optimization methods and software. Optim. Methods Softw. 39(3): 457-458 (2024) - [i20]Hai-Vy Nguyen, Fabrice Gamboa, Reda Chhaibi, Sixin Zhang, Serge Gratton, Thierry Giaccone:
Combining Statistical Depth and Fermat Distance for Uncertainty Quantification. CoRR abs/2404.08476 (2024) - [i19]Hai-Vy Nguyen, Fabrice Gamboa, Sixin Zhang, Reda Chhaibi, Serge Gratton, Thierry Giaccone:
Large Margin Discriminative Loss for Classification. CoRR abs/2405.18499 (2024) - [i18]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 abs/2406.17788 (2024) - [i17]Serge Gratton, Philippe L. Toint:
S2MPJ and CUTEst optimization problems for Matlab, Python and Julia. CoRR abs/2407.07812 (2024) - [i16]Serge Gratton, Chee-Khian Sim, Philippe L. Toint:
Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(ε-2) rather than 𝒪(ε-2). CoRR abs/2408.09124 (2024) - [i15]Victorita Dolean, Serge Gratton, Alexander Heinlein, Valentin Mercier:
Two-level deep domain decomposition method. CoRR abs/2408.12198 (2024) - 2023
- [j71]Serge Gratton, Philippe L. Toint:
OFFO minimization algorithms for second-order optimality and their complexity. Comput. Optim. Appl. 84(2): 573-607 (2023) - [j70]Serge Gratton, Sadok Jerad, Philippe L. Toint:
An adaptive regularization method in Banach spaces. Optim. Methods Softw. 38(6): 1163-1179 (2023) - [j69]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): 1621-1646 (2023) - [j68]Serge Gratton, Alena Kopanicáková, Philippe L. Toint:
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. SIAM J. Optim. 33(4): 2772-2800 (2023) - [i14]Serge Gratton, Alena Kopanicáková, Philippe L. Toint:
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training. CoRR abs/2302.07049 (2023) - [i13]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 abs/2305.14477 (2023) - [i12]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 abs/2311.06069 (2023) - 2022
- [j67]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): 361-386 (2022) - [j66]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): 1406-1422 (2022) - [i11]Serge Gratton, Sadok Jerad, Philippe L. Toint:
Parametric complexity analysis for a class of first-order Adagrad-like algorithms. CoRR abs/2203.01647 (2022) - 2021
- [j65]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): 1-24 (2021) - [j64]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) - [j63]Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur:
On High-Order Multilevel Optimization Strategies. SIAM J. Optim. 31(1): 307-330 (2021) - [i10]Mathis Peyron, Anthony Fillion, Selime Gürol, Victor Marchais, Serge Gratton, Pierre Boudier, Gaël Goret:
Latent Space Data Assimilation by using Deep Learning. CoRR abs/2104.00430 (2021) - [i9]Serge Gratton, Sadok Jerad, Philippe L. Toint:
Hölder Gradient Descent and Adaptive Regularization Methods in Banach Spaces for First-Order Points. CoRR abs/2104.02564 (2021) - [i8]Valentin Mercier, Serge Gratton, Pierre Boudier:
A coarse space acceleration of deep-DDM. CoRR abs/2112.03732 (2021) - 2020
- [j62]Serge Gratton, Philippe L. Toint:
A note on solving nonlinear optimization problems in variable precision. Comput. Optim. Appl. 76(3): 917-933 (2020) - [j61]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): 198-228 (2020) - [j60]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): 195-222 (2020) - [j59]Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur:
On Iterative Solution of the Extended Normal Equations. SIAM J. Matrix Anal. Appl. 41(4): 1571-1589 (2020) - [i7]Pierre Boudier, Anthony Fillion, Serge Gratton, Selime Gürol:
DAN - An optimal Data Assimilation framework based on machine learning Recurrent Networks. CoRR abs/2010.09694 (2020)
2010 – 2019
- 2019
- [j58]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): 525-559 (2019) - [i6]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 abs/1904.04685 (2019) - [i5]Serge Gratton, Ehouarn Simon, David Titley-Péloquin, Philippe L. Toint:
Exploiting variable precision in GMRES. CoRR abs/1907.10550 (2019) - [i4]Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur:
On the iterative solution of systems of the form ATA x=ATb+c. CoRR abs/1911.00026 (2019) - 2018
- [j57]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): 31-44 (2018) - [j56]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): 885-913 (2018) - [j55]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): 791-825 (2018) - [j54]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): 45-69 (2018) - [j53]Serge Gratton, David Titley-Péloquin:
Improved Bounds for Small-Sample Estimation. SIAM J. Matrix Anal. Appl. 39(2): 922-931 (2018) - [i3]Serge Gratton, Ehouarn Simon, Philippe L. Toint:
Minimizing convex quadratic with variable precision Krylov methods. CoRR abs/1807.07476 (2018) - [i2]Serge Gratton, Philippe L. Toint:
A note on solving nonlinear optimization problems in variable precision. CoRR abs/1812.03467 (2018) - 2017
- [j52]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): 533-554 (2017) - [j51]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): 895-922 (2017) - [j50]Serge Gratton, N. Soualmi, Luís Nunes Vicente:
An indicator for the switch from derivative-free to derivative-based optimization. Oper. Res. Lett. 45(4): 353-361 (2017) - [j49]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): 1100-1115 (2017) - 2016
- [j48]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): 924-951 (2016) - [j47]Serge Gratton, Pascal Hénon, Pavel Jiránek, Xavier Vasseur:
Reducing complexity of algebraic multigrid by aggregation. Numer. Linear Algebra Appl. 23(3): 501-518 (2016) - [j46]Serge Gratton, Jean Tshimanga Ilunga:
On a second-order expansion of the truncated singular subspace decomposition. Numer. Linear Algebra Appl. 23(3): 519-534 (2016) - [j45]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): 865-887 (2016) - 2015
- [j44]Youssef Diouane, Serge Gratton, Luís Nunes Vicente:
Globally convergent evolution strategies for constrained optimization. Comput. Optim. Appl. 62(2): 323-346 (2015) - [j43]Serge Gratton, M. Monserrat Rincon-Camacho, Ehouarn Simon, Philippe L. Toint:
Observation thinning in data assimilation computations. EURO J. Comput. Optim. 3(1): 31-51 (2015) - [j42]Youssef Diouane, Serge Gratton, Luís Nunes Vicente:
Globally convergent evolution strategies. Math. Program. 152(1-2): 467-490 (2015) - [j41]Serge Gratton, Vincent Malmedy, Philippe L. Toint:
Quasi-Newton updates with weighted secant equations. Optim. Methods Softw. 30(4): 748-755 (2015) - [j40]Serge Gratton, Clément W. Royer, Luís Nunes Vicente, Zaikun Zhang:
Direct Search Based on Probabilistic Descent. SIAM J. Optim. 25(3): 1515-1541 (2015) - [c5]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: 1080-1083 - 2014
- [j39]Serge Gratton, David Titley-Péloquin:
Stochastic Conditioning of Matrix Functions. SIAM/ASA J. Uncertain. Quantification 2(1): 763-783 (2014) - [j38]Serge Gratton, Luís Nunes Vicente:
A surrogate management framework using rigorous trust-region steps. Optim. Methods Softw. 29(1): 10-23 (2014) - [j37]Serge Gratton, Luís Nunes Vicente:
A Merit Function Approach for Direct Search. SIAM J. Optim. 24(4): 1980-1998 (2014) - [j36]Serge Gratton, David Titley-Péloquin, Philippe L. Toint, Jean Tshimanga Ilunga:
Differentiating the Method of Conjugate Gradients. SIAM J. Matrix Anal. Appl. 35(1): 110-126 (2014) - [j35]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): 1073-1085 (2014) - 2013
- [j34]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): 1-25 (2013) - [j33]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): 663-688 (2013) - [j32]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): 1257-1276 (2013) - [j31]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) - [c4]Marc Baboulin, Serge Gratton, Rémi Lacroix, Alan J. Laub:
Statistical Estimates for the Conditioning of Linear Least Squares Problems. PPAM (1) 2013: 124-133 - 2012
- [j30]Serge Gratton, Vincent Malmedy, Philippe L. Toint:
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Comput. Optim. Appl. 51(3): 967-979 (2012) - [j29]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): 2322-2336 (2012) - [j28]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): 822-836 (2012) - [j27]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) - 2011
- [j26]M'Barek Fares, Serge Gratton, Philippe L. Toint:
Fast regularized linear sampling for inverse scattering problems. Numer. Linear Algebra Appl. 18(1): 55-68 (2011) - [j25]Serge Gratton, Mélodie Mouffe, Philippe L. Toint:
Stopping rules and backward error analysis for bound-constrained optimization. Numerische Mathematik 119(1): 163-187 (2011) - [j24]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): 873-894 (2011) - [j23]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): 912-935 (2011) - [j22]Marc Baboulin, Serge Gratton:
A Contribution to the Conditioning of the Total Least-Squares Problem. SIAM J. Matrix Anal. Appl. 32(3): 685-699 (2011) - [j21]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): 969-986 (2011) - [j20]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): 1212-1235 (2011) - [c3]Antonio Mucherino, Martin Fuchs, Xavier Vasseur, Serge Gratton:
Variable Neighborhood Search for Robust Optimization and Applications to Aerodynamics. LSSC 2011: 230-237 - 2010
- [j19]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): 359-386 (2010) - [j18]Serge Gratton, Philippe L. Toint:
Approximate invariant subspaces and quasi-newton optimization methods. Optim. Methods Softw. 25(4): 507-529 (2010) - [j17]Luc Giraud, Serge Gratton, Xavier Pinel, Xavier Vasseur:
Flexible GMRES with Deflated Restarting. SIAM J. Sci. Comput. 32(4): 1858-1878 (2010) - [i1]Marc Baboulin, Serge Gratton:
A contribution to the conditioning of the total least squares problem. CoRR abs/1012.5484 (2010)
2000 – 2009
- 2009
- [j16]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): 517-533 (2009) - 2008
- [j15]Serge Gratton, Annick Sartenaer, Philippe L. Toint:
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization. SIAM J. Optim. 19(1): 414-444 (2008) - [j14]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): 13:1-13:12 (2008) - 2007
- [j13]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): 502-509 (2007) - [j12]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): 483-502 (2007) - [j11]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): 1167-1181 (2007) - [j10]Serge Gratton, Amos S. Lawless, Nancy K. Nichols:
Approximate Gauss-Newton Methods for Nonlinear Least Squares Problems. SIAM J. Optim. 18(1): 106-132 (2007) - [j9]Mario Arioli, Marc Baboulin, Serge Gratton:
A Partial Condition Number for Linear Least Squares Problems. SIAM J. Matrix Anal. Appl. 29(2): 413-433 (2007) - [j8]Luc Giraud, Serge Gratton, Julien Langou:
Convergence in Backward Error of Relaxed GMRES. SIAM J. Sci. Comput. 29(2): 710-728 (2007) - [j7]Bruno Carpentieri, Luc Giraud, Serge Gratton:
Additive and Multiplicative Two-Level Spectral Preconditioning for General Linear Systems. SIAM J. Sci. Comput. 29(4): 1593-1612 (2007) - [j6]Mario Arioli, Iain S. Duff, Serge Gratton, Stéphane Pralet:
A Note on GMRES Preconditioned by a Perturbed L D LT Decomposition with Static Pivoting. SIAM J. Sci. Comput. 29(5): 2024-2044 (2007) - 2006
- [j5]Luc Giraud, Serge Gratton:
On the Sensitivity of Some Spectral Preconditioners. SIAM J. Matrix Anal. Appl. 27(4): 1089-1105 (2006) - 2005
- [j4]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): 353-363 (2005) - [j3]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): 228-238 (2005) - 2004
- [j2]Luc Giraud, Serge Gratton, Julien Langou:
A Rank-k Update Procedure for Reorthogonalizing the Orthogonal Factor from Modified Gram-Schmidt. SIAM J. Matrix Anal. Appl. 25(4): 1163-1177 (2004) - [c2]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: 64-74 - 2003
- [c1]Eric Anterrieu, Serge Gratton, Bruno Picard:
Self characterization of modelling parameters for synthetic aperture imaging radiometers. IGARSS 2003: 3052-3054 - 2000
- [j1]Françoise Chaitin-Chatelin, Serge Gratton:
On the condition numbers associated with the polar factorization of a matrix. Numer. Linear Algebra Appl. 7(5): 337-354 (2000)
Coauthor Index
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