Associate professor in mathematics at EPFL
I run the chair of continuous optimization OPTIM at EPFL since July 2020.
My group works on optimization, statistical estimation and numerical analysis. Much of what we do is related to nonconvex optimization.
For Riemannian optimization in particular, we develop a toolbox called Manopt and I wrote a book.
My 2021 ERC Starting Grant project GEOSYM runs from fall 2022 to 2027. Our goal is to harness geometry, symmetry and statistics in optimization to tackle nonconvexity. This is funded by SERI.
As of Jan. 1st, 2022, I am an associate editor for Mathematical Programming.
The blog of my group is Race to the bottom.
Research topics:
Group members, past and present:
Positions prior to EPFL:
Bio sketch:
Nicolas Boumal studies continuous optimization, with a focus on nonconvexity and geometric structure. Much of his work is on the theory of algorithms and applications. On the software side, he develops the Manopt toolbox for optimization on manifolds. He blogs about optimization at RaceToTheBottom.xyz. He is an associate professor at EPFL and an associate editor for Mathematical Programming.
@Article{musat2026largesteps,
author = {Musat, A.-A. and Boumal, N.},
journal = {arXiv 2610.26748},
title = {Gradient descent reaches arbitrary accuracy in a fixed number of large steps on multiclass logistic regression},
year = {2026}
}
@Article{boumal2026globalpl,
author = {Boumal, N. and Criscitiello, C. and Rebjock, Q.},
journal = {arXiv 2604.07972},
title = {Smooth, globally {Polyak-{\L}ojasiewicz} functions are nonlinear least-squares},
year = {2026}
}
@Article{dragomir2026randomizedtr,
author = {Dragomir, R.-A. and Jiang, X. and Sun, B. and Boumal, N.},
journal = {arXiv 2603.15494},
title = {A practical randomized trust-region method to escape saddle points in high dimension},
year = {2026}
}
@Article{musat2026nonautonomous,
author = {Musat, A.-A. and Boumal, N.},
journal = {arXiv 2603.02782},
title = {A non-autonomous center-stable set theorem for saddle avoidance in optimization},
year = {2026}
}
@Article{gonon2026muon,
author = {Gonon, A. and Musat, A.-A. and Boumal, N.},
journal = {arXiv 2602.11948},
title = {Insights on {Muon} from simple quadratics},
year = {2026}
}
@Article{gonon2026gmc,
author = {Gonon, A. and Cordonnier, A. and Boumal, N.},
journal = {arXiv 2602.07562},
title = {Gaussian Match-and-Copy: A Minimalist Benchmark for Studying Transformer Induction},
year = {2026}
}
@Article{musat2026saddlelinesearch,
title = {Gradient Descent Avoids Strict Saddles with a Simple Line-Search Method Too},
DOI = {10.1287/moor.2025.1350},
journal = {Mathematics of Operations Research},
publisher = {Institute for Operations Research and the Management Sciences ({INFORMS})},
author = {Musat, Andreea-Alexandra and Boumal, Nicolas},
year = {2026}
}
@Article{criscitiello2026snl,
title = {Sensor network localization has a benign landscape after low-dimensional relaxation},
DOI = {10.1007/s10107-026-02380-y},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media LLC},
author = {Criscitiello, C. and McRae, A.D. and Rebjock, Q. and Boumal, N.},
year = {2026}
}
@Article{rebjock2026desingularization,
author = {Rebjock, Q. and Boumal, N.},
journal = {SIAM Journal on Optimization},
title = {Optimization over bounded-rank matrices through a desingularization enables joint global and local guarantees},
year = {2026},
volume = {36},
number = {4},
pages = {2031--2059},
doi = {10.1137/24M1672742}
}
@article{criscitiello2026synchcircles,
title = {Synchronization on circles and spheres with nonlinear interactions},
author = {Criscitiello, C. and Rebjock, Q. and McRae, A.D. and Boumal, N.},
journal = {SIAM Journal on Applied Dynamical Systems},
year = {2026},
doi = {10.1137/24M1699759},
volume = {25},
number = {2},
pages = {1207--1237}
}
@Article{mcrae2025benignnearexact,
author = {McRae, A.D. and Abdalla, P. and Bandeira, A.S. and Boumal, N.},
title = {Nonconvex landscapes for ${Z}_2$ synchronization and graph clustering are benign near exact recovery thresholds},
DOI = {10.1093/imaiai/iaaf012},
volume = {14},
number = {2},
journal = {Information and Inference: A Journal of the {IMA}},
publisher = {Oxford University Press ({OUP})},
year = {2025}
}
@Article{rebjock2024nonisolatedTRtCG,
author = {Rebjock, Q. and Boumal, N.},
title = {Fast convergence of trust-regions for non-isolated minima via analysis of {CG} on indefinite matrices},
journal = {Mathematical Programming},
publisher = {Springer},
doi = {10.1007/s10107-024-02140-w},
year = {2024}
}
@Article{rebjock2024nonisolated,
author = {Rebjock, Q. and Boumal, N.},
title = {Fast convergence to non-isolated minima: four equivalent conditions for {$C^2$} functions},
journal = {Mathematical Programming},
publisher = {Springer},
doi = {10.1007/s10107-024-02136-6},
year = {2024}
}
@Article{mcrae2024benignlowdim,
author = {McRae, A.D. and Boumal, N.},
journal = {SIAM Journal on Optimization},
title = {Benign landscapes of low-dimensional relaxations for orthogonal synchronization on general graphs},
year = {2024},
number = {2},
pages = {1427--1454},
volume = {34},
doi = {10.1137/23M1584642}
}
Congratulations to Eitan for his INFORMS Optimization Society 2024 Student Paper Prize!
@Article{levin2025lifts,
title = {The effect of smooth parametrizations on nonconvex optimization landscapes},
volume = {209},
DOI = {10.1007/s10107-024-02058-3},
number = {1--2},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media {LLC}},
author = {Levin, E. and Kileel, J. and Boumal, N.},
year = {2025},
pages = {63--111}
}
@Article{goyens2024fletcher,
author = {Goyens, F. and Eftekhari, A. and Boumal, N.},
title = {Computing second-order points under equality constraints: revisiting {F}letcher's augmented {L}agrangian},
journal = {Journal of Optimization Theory and Applications},
publisher = {Springer Science and Business Media LLC},
doi = {10.1007/s10957-024-02421-6},
year = {2024}
}
Cross-posted on bioRxiv.
@article{bendory2023toward,
author = {Bendory, T. and Boumal, N. and Leeb, W. and Levin, E. and Singer, A.},
title = {Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit},
journal = {SIAM Journal on Imaging Sciences},
volume = {16},
number = {2},
pages = {886--910},
year = {2023},
doi = {10.1137/22M1503828}
}
The arXiv version contains a few details omitted in the published version.
@Article{levin2023stationaryrank,
title = {Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy},
volume = {199},
DOI = {10.1007/s10107-022-01851-2},
number = {1--2},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media {LLC}},
author = {Levin, E. and Kileel, J. and Boumal, N.},
year = {2023},
month = jun,
pages = {831--864}
}
@Article{lan2022RCT,
author = {Lan, T.-Y. and Boumal, N. and Singer, A.},
journal = {Acta Crystallographica Section {A}},
title = {Random Conical Tilt Reconstruction without Particle Picking in Cryo-electron Microscopy},
year = {2022},
doi = {10.1107/s2053273322005071},
publisher = {International Union of Crystallography ({IUCr})},
volume = {78},
number = {4},
pages = {294--301},
}
@Article{criscitiello2023accelerated,
author = {Criscitiello, C. and Boumal, N.},
journal = {Journal of Foundations of Computational Mathematics},
title = {An accelerated first-order method for non-convex optimization on manifolds},
doi = {10.1007/s10208-022-09573-9},
publisher = {Springer Science and Business Media {LLC}},
year = {2023},
volume = {23},
number = {4},
pages = {1433--1509}
}
@Article{pumir2021procrustes,
author = {Pumir, T. and Singer, A. and Boumal, N.},
journal = {Information and {I}nference, a journal of the {IMA}},
title = {The generalized orthogonal {P}rocrustes problem in the high noise regime},
year = {2021},
doi = {10.1093/imaiai/iaaa035},
publisher = {Oxford University Press ({OUP})},
volume = {10},
number = {3},
pages = {921--954}
}
This is a significantly extended version of an earlier report. The former title was “Adaptive regularization with cubics on manifolds with a first-order analysis,” available as v1 on arXiv. A second major extension was posted as v3 on Nov. 7, 2019. Freely accessible published version here.
@article{agarwal2020arc,
author = {Agarwal, N. and Boumal, N. and Bullins, B. and Cartis, C.},
title = {Adaptive regularization with cubics on manifolds},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media {LLC}},
year = {2020},
doi = {10.1007/s10107-020-01505-1}
}
@article{lan2020multitargetdetection,
author = {Ti-Yen Lan and Tamir Bendory and Nicolas Boumal and Amit Singer},
title = {Multi-Target Detection With an Arbitrary Spacing Distribution},
journal = {{IEEE} Transactions on Signal Processing},
volume = {68},
pages = {1589--1601},
doi = {10.1109/tsp.2020.2975943},
year = {2020},
publisher = {{IEEE}}
}
@article{bendory2019multitargetdetection,
title = {Multi-target detection with application to cryo-electron microscopy},
author = {Tamir Bendory and Nicolas Boumal and William Leeb and Eitan Levin and Amit Singer},
journal = {Inverse Problems},
year = {2019},
month = {sep},
publisher = {{IOP} Publishing},
volume = {35},
number = {10},
pages = {104003},
doi = {10.1088/1361-6420/ab2aec}
}
@article{ma2020mra2D,
author = {Ma, C. and Bendory, T. and Boumal, N. and Sigworth, F. and Singer, A.},
title = {Heterogeneous multireference alignment for images with application to {2-D} classification in single particle reconstruction},
journal = {IEEE Transactions on Image Processing},
year = {2020},
pages = {1699--1710},
volume = {9},
issue = {1},
doi = {10.1109/TIP.2019.2945686}
}
@Article{liu2020riemannianconstraints,
author = {Liu, C. and Boumal, N.},
journal = {Applied Mathematics and Optimization},
title = {Simple algorithms for optimization on {R}iemannian manifolds with constraints},
year = {2020},
number = {3},
pages = {949--981},
volume = {82},
doi = {10.1007/s00245-019-09564-3},
publisher = {Springer Science and Business Media {LLC}},
}
@article{boumal2019deterministicbm,
author = {Boumal, N. and Voroninski, V. and Bandeira, A.S.},
title = {Deterministic Guarantees for {B}urer-{M}onteiro Factorizations of Smooth Semidefinite Programs},
journal = {Communications on Pure and Applied Mathematics},
volume = {73},
number = {3},
pages = {581--608},
year = {2019},
publisher = {Wiley},
doi = {10.1002/cpa.21830}
}
Extended from a shorter preprint titled “Renegar’s Condition Number and Compressed Sensing Performance”.
@article{roulet2020renegar,
author = {Roulet, V. and Boumal, N. and d'Aspremont, A.},
title = {Computational Complexity versus Statistical Performance on Sparse Recovery Problems},
journal = {Information and {I}nference: A Journal of the {IMA}},
year = {2020},
doi = {10.1093/imaiai/iay020},
pages = {1--32},
volume = {9},
number = {1},
publisher = {Oxford University Press ({OUP})}
}
@Article{bendory2018stft,
author = {Bendory, T. and Eldar, Y.C. and Boumal, N.},
title = {Non-convex phase retrieval from {STFT} measurements},
journal = {IEEE Transactions on Information Theory},
year = {2018},
volume = {64},
number = {1},
pages = {467--484},
month = jan,
doi = {10.1109/TIT.2017.2745623},
}
Typo: eq. (VI.1), \(\log p(X, r | x_k)\) should be \(\log p(X, r | x)\) instead.
@Article{bendory2018bispectruminversion,
author = {Bendory, T. and Boumal, N. and Ma, C. and Zhao, Z. and Singer, A.},
title = {Bispectrum Inversion With Application to Multireference Alignment},
journal = {IEEE Transactions on Signal Processing},
year = {2018},
volume = {66},
number = {4},
pages = {1037--1050},
doi = {10.1109/TSP.2017.2775591}
}
Congratulations to Yiqiao (Joe) for his SIAM best student paper prize!
@article{zhong2018nearoptimal,
author = {Zhong, Y. and Boumal, N.},
title = {Near-optimal bounds for phase synchronization},
journal = {SIAM Journal on Optimization},
year = {2018},
volume = {28},
number = {2},
pages = {989--1016},
doi = {10.1137/17M1122025}
}
@Article{boumal2018globalrates,
author = {Boumal, N. and Absil, P.-A. and Cartis, C.},
journal = {{IMA} Journal of Numerical Analysis},
title = {Global rates of convergence for nonconvex optimization on manifolds},
year = {2018},
month = feb,
number = {1},
pages = {1--33},
volume = {39},
doi = {10.1093/imanum/drx080},
publisher = {Oxford University Press ({OUP})},
}
@Article{boumal2016nonconvexphase,
author = {Boumal, N.},
title = {Nonconvex Phase Synchronization},
journal = {SIAM Journal on Optimization},
volume = {26},
number = {4},
pages = {2355--2377},
year = {2016},
doi = {10.1137/16M105808X}
}
Submitted Nov. 2014. Updated Oct. 2015, with a better rate and simpler proof. Accepted in July 2016.
@Article{bandeira2016tightness,
Title = {Tightness of the maximum likelihood semidefinite relaxation for angular synchronization},
Author = {Bandeira, A.S. and Boumal, N. and Singer, A.},
Journal = {Mathematical Programming},
Year = {2017},
pages = {145--167},
volume = {163},
number = {1},
doi = {10.1007/s10107-016-1059-6}
}
Former title: Low-rank matrix completion via trust-regions on the Grassmann manifold
@article{boumal2015rtrmcextended,
Title = {Low-rank matrix completion via preconditioned optimization on the {G}rassmann manifold},
Author = {Boumal, N. and Absil, P.-A.},
Journal = {Linear Algebra and its Applications},
Year = {2015},
Pages = {200--239},
Volume = {475},
Doi = {10.1016/j.laa.2015.02.027},
Url = {http://www.sciencedirect.com/science/article/pii/S0024379515001342}
}
@Article{taquet2015improved,
Title = {Improved fidelity of brain microstructure mapping from single-shell diffusion {MRI}},
Author = {Taquet, M. and Scherrer, B. and Boumal, N. and Peters, J.M. and Macq, B. and Warfield, S.K.},
Journal = {Medical Image Analysis },
Year = {2015},
Number = {1},
Pages = {268--286},
Volume = {26},
Doi = {10.1016/j.media.2015.10.004}
}
@Article{manopt,
author = {Boumal, N. and Mishra, B. and Absil, P.-A. and Sepulchre, R.},
journal = {Journal of Machine Learning Research},
title = {{M}anopt, a {M}atlab Toolbox for Optimization on Manifolds},
year = {2014},
number = {42},
pages = {1455--1459},
volume = {15},
url = {https://www.manopt.org},
}
Former title: Expected performance bounds for estimation on graphs from random relative measurements.
@article{boumal2014kirchhoff,
Title = {Concentration of the {K}irchhoff index for {E}rdos-{R}enyi graphs},
Author = {Boumal, N. and Cheng, X.},
Journal = {Systems and Control Letters},
Year = {2014},
Pages = {74--80},
Volume = {74},
Doi = {10.1016/j.sysconle.2014.10.006},
Url = {http://www.sciencedirect.com/science/article/pii/S016769111400228X}
}
Second prize at the Information and Inference best paper prize.
@article{boumal2014crbsynch,
author = {Boumal, N. and Singer, A. and Absil, P.-A. and Blondel, V.D.},
title = {{C}ram{\'e}r-{R}ao bounds for synchronization of rotations},
journal = {Information and Inference},
year = {2014},
volume = {3},
pages = {1--39},
doi = {10.1093/imaiai/iat006},
eprint = {http://imaiai.oxfordjournals.org/content/early/2013/09/23/imaiai.iat006.full.pdf+html},
url = {http://imaiai.oxfordjournals.org/content/3/1/1}
}
@article{borckmans2013riemannian,
title = "A {R}iemannian subgradient algorithm for economic dispatch with valve-point effect",
journal = "Journal of Computational and Applied Mathematics ",
volume = "255",
pages = "848--866",
year = "2014",
note = "",
issn = "0377-0427",
doi = "http://dx.doi.org/10.1016/j.cam.2013.07.002",
url = "http://www.sciencedirect.com/science/article/pii/S0377042713003464",
author = "Pierre B. Borckmans and S. Easter Selvan and Nicolas Boumal and P.-A. Absil",
}
@ARTICLE{boumal2013intrinsiccrb,
author={Boumal, N.},
journal={Signal Processing, IEEE Transactions on},
title={On Intrinsic {C}ram{\'e}r-{R}ao Bounds for {R}iemannian Submanifolds and Quotient Manifolds},
year={2013},
volume={61},
number={7},
pages={1809--1821},
doi={10.1109/TSP.2013.2242068},
ISSN={1053-587X}
}
@article{demanet2012probing,
title = {Matrix probing: A randomized preconditioner for the wave-equation {H}essian},
author = "Demanet, L. and Létourneau, P.-D. and Boumal, N. and Calandra, H. and Chiu, J. and Snelson, S.",
journal = "Applied and Computational Harmonic Analysis",
volume = "32",
number = "2",
pages = "155--168",
year = "2012",
issn = "1063-5203",
doi = "http://dx.doi.org/10.1016/j.acha.2011.03.006",
}
@InProceedings{criscitiello2023curvaturecomplexity,
title = {Curvature and complexity: Better lower bounds for geodesically convex optimization},
author = {Criscitiello, C. and Boumal, N.},
booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory},
pages = {2969--3013},
year = {2023},
editor = {Neu, G. and Rosasco, L.},
volume = {195},
series = {Proceedings of Machine Learning Research},
month = {12--15 Jul},
publisher = {PMLR},
url = {https://proceedings.mlr.press/v195/criscitiello23a.html}
}
An extended version is available on arXiv as v2 (parts were removed in v3, now published in our COLT 2023 paper). Congratulations to Chris for the ICCOPT 2022 Best Paper for Young Researchers Prize!
@InProceedings{criscitiello2022negativecurvature,
title = {Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles},
author = {Criscitiello, C. and Boumal, N.},
booktitle = {Proceedings of Thirty Fifth Conference on Learning Theory},
pages = {496--542},
year = {2022},
editor = {Loh, P.-L. and Raginsky, M.},
volume = {178},
series = {Proceedings of Machine Learning Research},
month = {02--05 Jul},
publisher = {PMLR},
url = {https://proceedings.mlr.press/v178/criscitiello22a.html}
}
@InProceedings{scieur2021quasinewton,
title = {Generalization of Quasi-{N}ewton Methods: Application to Robust Symmetric Multisecant Updates},
author = {Scieur, D. and Liu, L. and Pumir, T. and Boumal, N.},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {550--558},
year = {2021},
editor = {Banerjee, A. and Fukumizu, K.},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {{PMLR}},
pdf = {http://proceedings.mlr.press/v130/scieur21a/scieur21a.pdf},
url = {http://proceedings.mlr.press/v130/scieur21a.html},
}
@Article{psenka2020secondorderttrank,
author = {Psenka, M. and Boumal, N.},
journal = {NeurIPS Optimization workshop, arXiv 2011.13395},
title = {Second-order optimization for tensors with fixed tensor-train rank},
year = {2020}
}
@InCollection{criscitiello2019escapingsaddles,
author = {Criscitiello, C. and Boumal, N.},
title = {Efficiently escaping saddle points on manifolds},
booktitle = {Advances in Neural Information Processing Systems 32},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d'Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {5985--5995},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/8832-efficiently-escaping-saddle-points-on-manifolds}
}
Oral presentation, one of 30 among 1100 accepted papers.
@incollection{pumir2018smoothedsmoothsdp,
author = {Pumir, T. and Jelassi, S. and Boumal, N.},
title = {Smoothed analysis of the low-rank approach for smooth semidefinite programs},
booktitle = {Advances in Neural Information Processing Systems 31},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {2283--2292},
year = {2018},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/7496-smoothed-analysis-of-the-low-rank-approach-for-smooth-semidefinite-programs.pdf}
}
Featured in an interview on Dustin Mixon’s blog.
@InProceedings{bhojanapalli2018smoothedsdp,
title = {Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form},
author = {Bhojanapalli, S. and Boumal, N. and Jain, P. and Netrapalli, P.},
booktitle = {Proceedings of the 31st {C}onference {O}n {L}earning {T}heory},
pages = {3243--3270},
year = {2018},
editor = {Bubeck, S. and Perchet, V. and Rigollet, P.},
volume = {75},
series = {Proceedings of Machine Learning Research},
address = {},
month = {06--09 Jul},
publisher = {PMLR},
url = {http://proceedings.mlr.press/v75/bhojanapalli18a.html}
}
congratulations to Eitan for the best student paper prize!
@InProceedings{levin2018abinitio,
author = {Levin, E. and Bendory, T. and Boumal, N. and Kileel, J. and Singer, A.},
title = {{3D} ab initio modeling in cryo-{EM} by autocorrelation analysis},
booktitle = {2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018)},
year = {2018},
pages = {1569--1573},
month = {April},
doi = {10.1109/ISBI.2018.8363873}
}
@InProceedings{boumal2018heterogeneous,
author = {Boumal, N. and Bendory, T. and Lederman, R.R. and Singer, A.},
title = {Heterogeneous multireference alignment: A single pass approach},
booktitle = {2018 52nd Annual Conference on Information Sciences and Systems ({CISS})},
year = {2018},
pages = {1--6},
month = {March},
doi = {10.1109/CISS.2018.8362313}
}
An extension of this paper appears in Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs.
@incollection{boumal2016bmapproach,
author = {Boumal, N. and Voroninski, V. and Bandeira, A.S.},
title = {The non-convex {B}urer--{M}onteiro approach works on smooth semidefinite programs},
booktitle = {Advances in Neural Information Processing Systems 29},
editor = {D. D. Lee and M. Sugiyama and U. V. Luxburg and I. Guyon and R. Garnett},
pages = {2757--2765},
year = {2016},
publisher = {Curran Associates, Inc.}
}
Featured in an interview on Dustin Mixon’s blog.
@inproceedings{bandeira2016lowrankmaxcut,
author = {Bandeira, A.S. and Boumal, N. and Voroninski, V.},
title = {On the low-rank approach for semidefinite programs arising in synchronization and community detection},
booktitle = {Proceedings of The 29th Conference on Learning Theory, {COLT} 2016,
New York, NY, June 23--26},
pages = {361--382},
year = {2016}
}
@InCollection{boumal2015rtrfd,
Title = {{R}iemannian Trust Regions with Finite-Difference {H}essian Approximations are Globally Convergent},
Author = {Boumal, N.},
Booktitle = {{G}eometric {S}cience of {I}nformation},
Publisher = {Springer International Publishing},
Year = {2015},
Editor = {Nielsen, F. and Barbaresco, F.},
Pages = {467--475},
Series = {Lecture Notes in Computer Science},
Volume = {9389},
Doi = {10.1007/978-3-319-25040-3_50},
Keywords = {RTR-FD; Optimization on manifolds; Convergence; Manopt}
}
Typo: the upperbound on the MSE (as given just before section IV.B) is \(2\pi^2/3 + 4\), not \(2\pi^2/4 + 3\) as stated in the published version.
@inproceedings{boumal2013MLE,
author={Boumal, N. and Singer, A. and Absil, P.-A.},
booktitle={{Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on}},
title={Robust estimation of rotations from relative measurements by maximum likelihood},
year={2013},
month={Dec},
pages={1156--1161},
doi={10.1109/CDC.2013.6760038},
ISSN={0743-1546}
}
@incollection{taquet2013multifascicle,
year={2013},
isbn={978-3-642-40810-6},
booktitle={Medical Image Computing and Computer-Assisted Intervention - MICCAI 2013},
volume={8149},
series={Lecture Notes in Computer Science},
editor={Mori, K. and Sakuma, I. and Sato, Y. and Barillot, C. and Navab, N.},
doi={10.1007/978-3-642-40811-3_87},
title={Estimation of a Multi-fascicle Model from Single B-Value Data with a Population-Informed Prior},
url={http://dx.doi.org/10.1007/978-3-642-40811-3_87},
publisher={Springer Berlin Heidelberg},
keywords={Diffusion; Single-Shell; Generative Models; Estimation},
author={Taquet, M. and Scherrer, B. and Boumal, N. and Macq, B. and Warfield, S.K.},
pages={695--702}
}
@incollection{boumal2013rotations,
author={Boumal, N.},
title={Interpolation and Regression of Rotation Matrices},
year={2013},
booktitle={Geometric Science of Information},
volume={8085},
series={Lecture Notes in Computer Science},
editor={Nielsen, F. and Barbaresco, F.},
doi={10.1007/978-3-642-40020-9_37},
publisher={Springer Berlin Heidelberg},
keywords={optimization on manifolds; non-parametric regression; denoising of rotations; video stabilization; 3D motion planning},
pages={345--352}
}
An extended version is available: see full papers. This work was presented as a poster.
@incollection{boumal2011rtrmc,
title={{RTRMC}: A {R}iemannian trust-region method for low-rank matrix completion},
author={Boumal, N. and Absil, P.-A.},
booktitle={Advances in Neural Information Processing Systems 24 ({NIPS})},
editor={J. Shawe-Taylor and R.S. Zemel and P. Bartlett and F.C.N. Pereira and K.Q. Weinberger},
pages={406--414},
year = {2011}
}
This work was presented as a poster.
@inproceedings{boumal2011icassp,
title={Discrete regression methods on the cone of positive-definite matrices},
author={Boumal, N. and Absil, P.-A.},
booktitle={Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on},
pages={4232--4235},
year={2011},
organization={IEEE}
}
@inproceedings{boumal2011ifac,
author = {Boumal, N. and Absil, P.-A.},
title = {A discrete regression method on manifolds and its application to data on {SO(n)}},
booktitle = {Proceedings of the 18th IFAC World Congress (Milan)},
volume={18},
number={1},
pages={2284--2289},
year = {2011}
}
This is a technical report. The core theoretical results appear (generalized) in Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs.
@article{boumal2015staircase,
author = {Boumal, N.},
title = {A {R}iemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints},
journal = {arXiv preprint arXiv:1506.00575},
year = {2015}
}
@phdthesis{boumal2014thesis,
author = {Boumal, N.},
title = {Optimization and estimation on manifolds},
school = {Universit\'e catholique de Louvain},
year = {2014},
month = {feb}
}
@mastersthesis{boumal2010discrete,
author = {Boumal, N.},
title = {Discrete curve fitting on manifolds},
school = {Universit\'e catholique de Louvain},
year = {2010},
month = {jun}
}
This was a blackboard talk.
These were whiteboard talks.
This is an old presentation about www.manopt.org.
This book about optimization on smooth manifolds has no prerequisites in geometry or optimization. Chapters 3 and 5 can serve as a standalone introduction to differential and Riemannian geometry, focused on embedded submanifolds of linear spaces, with full proofs and an emphasis on computability. It then builds from there to equip the reader to take on modern research challenges.
Published by Cambridge University Press.
You may also be interested in the Manopt toolboxes (Matlab, Python, Julia).
Table of contents ()
Nicolas Boumal
EPFL SB MATH
MA C2 627 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Switzerland
Office: MA C2 627, 2nd floor
If you don't have a badge, use MA building entrance near Satellite (two levels above ground floor) and walk all the way to the end of the corridor.
E-mail: nicolas.boumal@epfl.ch
My Erdös number is 3, courtesy of two co-authors (Vincent Blondel and Afonso Bandeira).
Research will get you places! It got me in: Palo Alto, Boston, Princeton, London, Prague, Cannes, Lisbon, Milan, Dagstuhl, Granada, Sierra Nevada, Valencia, Berlin, Les Houches, Costa da Caparica, Paris, Florence, San Diego, Bordeaux, Montréal, Bonn, Pittsburgh, Oxford, Geneva, New York City, Barcelona, Chicago, Vancouver, Ames, Minneapolis, Washington DC, Stockholm, Lausanne, Oaxaca, Villars-sur-Ollon, Pasadena, Interlaken, Chexbres, Zurich, Seattle, Lugano, Biel, Lyon, Grenoble, Edinburgh, Saint Malo, Leysin, Vienna… and various places in Belgium (Louvain-la-Neuve, Leuven, Liège, La Roche, Mons, Knokke, Daverdisse, Spa, Namur, Bruxelles…).
SIAM Activity Group on Optimization Best Paper Prize 2026