André Uschmajew
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany
Office: G3 08
Contact:
Email
Phone:
+49 341 9959 824
Fax:
+49 341 9959 658
André Uschmajew
News & Activities
- I am a guest editor for a Research Topic on High-Performance Tensor Computations in Scientific Computing and Data Science in Frontiers in Applied Mathematics and Statistics. The submission deadline is November 1, 2021.
- Past events:
Workshop: Hierarchical Numerical Methods for PDEs, September 28-29, 2021 at MPI Leipzig
Mathematical Foundations and Algorithms for Tensor Computations, May 3 -7, 2021, at IPAM, Online
GAMM AG Workshop Computational and Mathematical Methods in Data Science (COMinDS 2020), September 10 - 11, 2020, Online
Low-rank Optimization and Applications 2019, April 01 - 05, 2019, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Nonsmooth Optimization and its Applications, May 15 - 19, 2017, Hausdorff Center for Mathematics, University of Bonn, Germany
Low-rank Optimization and Applications 2015, June 08 - 12, 2015, Hausdorff Center for Mathematics, University of Bonn, Germany
About
I am Max Planck Research Group Leader for the group Tensors and Optimization at MPI MiS in Leipzig.
My research is on low-rank approximation of matrices and tensors, multivariate functions, and high-dimensional equations. I am particularly interested in the algebraic and geometric structures that underlie multilinear representations of low-rank matrix and tensor manifolds, and their implications on the applicability and convergence of numerical optimization methods.
Academic CV:
- since Oct. 2017: Max Planck Research Group Leader at MPI MiS, Leipzig, Germany
- 2019 and 2020 Visiting professor at Leipzig University, Germany
- 2014 - 2017 Bonn Junior Fellow Professor at University of Bonn, Germany
- 2013 - 2014 Postdoc at EPF Lausanne, Switzerland
- 2008 - 2012 PhD at TU Berlin
I am an associate editor of Linear Algebra and Its Applications (LAA) and of Numerical Algebra, Control and Optimization (NACO).
I am a co-initiator of the Mathematics of Data Initiative at MPI MiS.
Publications
Preprints
H. Eisenmann ; F. Krahmer ; M. Pfeffer and A. Uschmajew:
Riemannian thresholding methods for row-sparse and low-rank matrix recovery.
Bibtex MIS-Preprint: 4/2021 [ARXIV] Repository Open Access
H. Eisenmann and A. Uschmajew:
Maximum relative distance between symmetric rank-two and rank-one tensors.
Bibtex MIS-Preprint: 27/2021 [ARXIV] Repository Open Access
I. V. Oseledets ; M. Rakhuba and A. Uschmajew:
Local convergence of alternating low-rank optimization methods with overrelaxation.
Bibtex MIS-Preprint: 29/2021 [ARXIV] Repository Open Access
Books
S. Hosseini ; B. S. Mordukhovich and A. Uschmajew (eds.):
Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization
and its Applications', Bonn, Germany, May 15-19, 2017.
Springer Birkhäuser, 2019. - VII, 149 p.
(International series of numerical mathematics ; 170)
ISBN 978-3-030-11369-8 Bibtex [DOI]
Journal articles and proceedings
A. Uschmajew and B. Vandereycken:
A note on the optimal convergence rate of descent methods with fixed step sizes for
smooth strongly convex functions.
Journal of optimization theory and applications,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 17/2021 [DOI] [ARXIV] Journal Open Access
M. Bachmayr ; H. Eisenmann ; E. Kieri and A. Uschmajew:
Existence of dynamical low-rank approximations to parabolic problems.
Mathematics of computation,
90 (2021) 330, p. 1799-1830 Bibtex MIS-Preprint: 33/2020 [DOI] [ARXIV] Repository Open Access
W. Hackbusch and A. Uschmajew:
Modified iterations for data-sparse solution of linear systems.
Vietnam journal of mathematics,
49 (2021) 2, p. 493-512 Bibtex MIS-Preprint: 58/2020 [DOI] Journal Open Access
C. Krumnow ; M. Pfeffer and A. Uschmajew:
Computing eigenspaces with low rank constraints.
SIAM journal on scientific computing,
43 (2021) 1, p. A586-A608 Bibtex MIS-Preprint: 102/2019 [DOI] Repository Open Access
T. Lehmann ; M. v.
Renesse ; A. Sambale and A. Uschmajew:
A note on overrelaxation in the Sinkhorn algorithm.
Optimization letters,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 110/2020 [DOI] [ARXIV] Journal Open Access
A. Agrachev ; K. Kozhasov and A. Uschmajew:
Chebyshev polynomials and best rank-one approximation ratio.
SIAM journal on matrix analysis and applications,
41 (2020) 1, p. 308-331 Bibtex MIS-Preprint: 34/2019 [DOI] [ARXIV] [PDF] Repository Open Access
A.-H. Phan ; A. Cichocki ; A. Uschmajew ; P. Tichavsky ; G. Luta and D. Mandic:
Tensor networks for latent variable analysis : novel algorithms for tensor train approximation.
IEEE transactions on neural networks and learning systems,
31 (2020) 11, p. 4622-4636 Bibtex [DOI] [ARXIV] Repository Open Access
A. Uschmajew ; M. Bachmayr ; H. Eisenmann and E. Kieri:
Dynamical low-rank approximation for parabolic problems [In: Mini-workshop : computational
optimization on manifolds ; 15 November - 21 November 2020 ; report no. 36/2020].
Oberwolfach reports,
17 (2020) 4, p. 1800-1802 Bibtex [DOI] [FREELINK] Repository Open Access
A. Uschmajew and B. Vandereycken:
On critical points of quadratic low-rank matrix optimization problems.
IMA journal of numerical analysis,
40 (2020) 4, p. 2626-2651 Bibtex MIS-Preprint: 58/2018 [DOI] Journal Open Access
A. Uschmajew and B. Vandereycken:
Geometric methods on low-rank matrix and tensor manifolds.
Handbook of variational methods for nonlinear geometric data / P.
Grohs... (eds.). Springer, 2020. - P. 261-313 Bibtex [DOI] [PDF] Journal Open Access
S. Hosseini ; D. R.
Luke and A. Uschmajew:
Tangent and normal cones for low-rank matrices.
Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization
and its Applications', Bonn, Germany, May 15-19, 2017 / S.
Hosseini... (eds.). Springer Birkhäuser, 2019. - P. 45-53
(International series of numerical mathematics ; 170)
Bibtex [DOI] [FREELINK] Repository Open Access
S. Hosseini and A. Uschmajew:
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank
optimization.
SIAM journal on optimization,
29 (2019) 4, p. 2853-2880 Bibtex [DOI] [PDF] Repository Open Access
M. Pfeffer ; A. Uschmajew ; A. Amaro and U. Pfeffer:
Data fusion techniques for the integration of multi-domain genomic data from uveal
melanoma.
Cancers,
11 (2019) 10, 1434 Bibtex MIS-Preprint: 42/2019 [DOI] Journal Open Access
Z. Li ; Y. Nakatsukasa ; T. Soma and A. Uschmajew:
On orthogonal tensors and best rank-one approximation ratio.
SIAM journal on matrix analysis and applications,
39 (2018) 1, p. 400-425 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
I. V. Oseledets ; M. Rakhuba and A. Uschmajew:
Alternating least squares as moving subspace correction.
SIAM journal on numerical analysis,
56 (2018) 6, p. 3459-3479 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
W. Hackbusch ; D. Kressner and A. Uschmajew:
Perturbation of higher-order singular values.
SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 374-387 Bibtex MIS-Preprint: 51/2016 [DOI] [PDF] Journal Open Access
W. Hackbusch and A. Uschmajew:
On the interconnection between the higher-order singular values of real tensors.
Numerische Mathematik,
135 (2017) 3, p. 875-894 Bibtex MIS-Preprint: 62/2015 [DOI] Journal Open Access
S. Hosseini and A. Uschmajew:
A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds.
SIAM journal on optimization,
27 (2017) 1, p. 173-189 Bibtex [DOI] [PDF] Repository Open Access
Y. Nakatsukasa ; T. Soma and A. Uschmajew:
Finding a low-rank basis in a matrix subspace.
Mathematical programming,
162 (2017) 1-2, p. 325-361 Bibtex [DOI] [ARXIV] Repository Open Access
M. Bachmayr ; R. Schneider and A. Uschmajew:
Tensor networks and hierarchical tensors for the solution of high-dimensional partial
differential equations.
Foundations of computational mathematics,
16 (2016) 6, p. 1423-1472 Bibtex [DOI] [PDF] Repository Open Access
L. Karlsson ; D. Kressner and A. Uschmajew:
Parallel algorithms for tensor completion in the CP format.
Parallel computing,
57 (2016), p. 222-234 Bibtex [DOI] [PDF] Repository Open Access
D. Kressner and A. Uschmajew:
On low-rank approximability of solutions to high-dimensional operator equations and
eigenvalue problems.
Linear algebra and its applications,
493 (2016), p. 556-572 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
R. Schneider and A. Uschmajew:
Convergence results for projected line-search methods on varieties of low-rank matrices
via Łojasiewicz inequality.
SIAM journal on optimization,
25 (2016) 1, p. 622-646 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
Z. Li ; A. Uschmajew and S. Zhang:
On convergence of the maximum block improvement method.
SIAM journal on optimization,
25 (2015) 1, p. 210-233 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew:
A new convergence proof for the higher-order power method and generalizations.
Pacific journal of optimization : an international journal,
11 (2015) 2, p. 309-321 Bibtex [ARXIV] [FREELINK] [PDF] Repository Open Access
A. Uschmajew:
Some results concerning rank-one truncated steepest descent directions in tensor spaces.
2015 International conference on sampling theory and applications (SampTA) took place
May 25-29, 2015 in Washington, DC, USA IEEE, 2015. - P. 415-419 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew and B. Vandereycken:
Greedy rank updates combined with Riemannian descent methods for low-rank optimization.
2015 International conference on sampling theory and applications (SampTA) took place
May 25-29, 2015 in Washington, DC, USA IEEE, 2015. - P. 420-424 Bibtex [DOI] [PDF] Repository Open Access
D. Kressner ; M. Steinlechner and A. Uschmajew:
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems.
SIAM journal on scientific computing,
36 (2014) 5, p. A2346-A2368 Bibtex [DOI] [PDF] Repository Open Access
R. Schneider and A. Uschmajew:
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces.
Journal of complexity,
30 (2014) 2, p. 56-71 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew and B. Vandereycken:
Line-search methods and rank increase on low-rank matrix varieties.
2014 International symposium on nonlinear theory and its applications : NOLTA2014,
Luzern, Switzerland, September 14-18, 2014 IEICE, 2014. - P. 52-55 Bibtex [FREELINK] [PDF] Repository Open Access
T. Rohwedder and A. Uschmajew:
On local convergence of alternating schemes for optimization of convex problems in
the tensor train format.
SIAM journal on numerical analysis,
51 (2013) 2, p. 1134-1162 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew ; D. Kressner and M. Steinlechner:
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems
[In: Numerical solution of PDE eigenvalue problems ; 17 November - 23 November 2013
; report no. 56/2013].
Oberwolfach reports,
10 (2013) 4, p. 3296-3298 Bibtex [DOI] [FREELINK] Repository Open Access
A. Uschmajew and B. Vandereycken:
The geometry of algorithms using hierarchical tensors.
Linear algebra and its applications,
439 (2013) 1, p. 133-166 Bibtex [DOI] [PDF] Repository Open Access
S. R.
Chinnamsetty ; H. Luo ; W. Hackbusch ; H.-J. Flad and A. Uschmajew:
Bridging the gap between quantum Monte Carlo and F12-methods.
Chemical physics,
401 (2012), p. 36-44 Bibtex MIS-Preprint: 68/2011 [DOI] [PDF] Repository Open Access
A. Uschmajew:
Local convergence of the alternating least squares algorithm for canonical tensor
approximation.
SIAM journal on matrix analysis and applications,
33 (2012) 2, p. 639-652 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew:
Regularity of tensor product approximations to square integrable functions.
Constructive approximation,
34 (2011) 3, p. 371-391 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew:
The regularity of tensor product approximations in \(L^2\) in dependence of the target
function [In: Mathematical methods in quantum chemistry ; June 26 th - July 2nd, 2011
; report no. 32/2011].
Oberwolfach reports,
8 (2011) 2, p. 1802-1804 Bibtex [DOI] [FREELINK] Repository Open Access
A. Uschmajew:
Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal
tensor product approximations.
Numerische Mathematik,
115 (2010) 2, p. 309-331 Bibtex [DOI] [PDF] Repository Open Access