Tensors and Optimization
Head:
André Uschmajew (Email)
Phone:
+49 (0) 341 - 9959 - 824
Fax:
+49 (0) 341 - 9959 - 658
Address:
Inselstr. 22
04103 Leipzig
Publications André Uschmajew
Preprints
M. Dressler ; A. Uschmajew and V. Chandrasekaran:
Kronecker product approximation of operators in spectral norm via alternating SDP.
Bibtex MIS-Preprint: 21/2022 [ARXIV] Repository Open Access
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
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
I. V. Oseledets ; M. Rakhuba and A. Uschmajew:
Local convergence of alternating low-rank optimization methods with overrelaxation.
Numerical linear algebra with applications,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 29/2021 [DOI] [ARXIV] Repository Open Access
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,
194 (2022) 1, p. 364-373 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
Thesis
