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.
Instructor then assistant professor in the mathematics department at Princeton University. There, I also interacted closely with PACM (the program in applied and computational mathematics), especially the group of Amit Singer. (Feb. 2016–June 2020);
Postdoc at Inria in Paris, affiliated with the computer science department of the Ecole Normale Supérieure with Alexandre d’Aspremont in the SIERRA team, working on topics at the intersection of optimization and statistics. (Oct. 2014–Jan. 2016);
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}
}
C. Criscitiello, A.D. McRae, Q. Rebjock and N. Boumal,
@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}
}
C. Criscitiello, Q. Rebjock, A.D. McRae and N. Boumal,
@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}
}
A.D. McRae, P. Abdalla, A.S. Bandeira and N. Boumal,
@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}
}
@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}
}
T. Bendory, N. Boumal, W. Leeb, E. Levin and A. Singer,
@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}
}
@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}}
}
T. Bendory, N. Boumal, W. Leeb, E. Levin and A. Singer,
@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}
}
C. Ma, T. Bendory, N. Boumal, F. Sigworth and A. Singer,
@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}
}
@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},
}
T. Bendory, N. Boumal, C. Ma, Z. Zhao and A. Singer,
@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}
}
@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{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}
}
@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}
}
M. Taquet, B. Scherrer, N. Boumal, J. Peters, B. Macq and S. Warfield,
@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}
}
N. Boumal, B. Mishra, P.-A. Absil and R. Sepulchre,
@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},
}
@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}
}
N. Boumal, A. Singer, P.-A. Absil and V.D. Blondel,
@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}
}
P.B. Borckmans, S.E. Selvan, N. Boumal and P.-A. Absil,
@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{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{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}
}
@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}
}
S. Bhojanapalli, N. Boumal, P. Jain and P. Netrapalli,
@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}
}
E. Levin, T. Bendory, N. Boumal, J. Kileel and A. Singer,
@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}
}
N. Boumal, T. Bendory, R. R. Lederman and A. Singer,
@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}
}
@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.}
}
@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}
}
@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}
}
M. Taquet, B. Scherrer, N. Boumal, B. Macq and S.K. Warfield,
@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}
}
@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}
}
@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.
@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}
}
2011, May 26 · 36th International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic
Inversion of the wave equation Hessian via discrete symbol calculus
(with L. Demanet)
2009, Oct. 16 · Total SA Mathias conference, Cannes, France
An introduction to optimization on smooth manifolds
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.
Junior seminar (optimization on manifolds, MAT982), Spring 2018
Junior seminar (math of data science through cryo-electron microscopy, MAT982), Fall 2018
Junior seminar (math of data science, MAT982), Fall 2019
Optimization on smooth manifolds (graduate course, MAT588), Spring 2019, 2020, book + videos
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.
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