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
A.
Agrachev ; K.
Kozhasov and A. Uschmajew:
Chebyshev polynomials and best rank-one approximation ratio.
Bibtex MIS-Preprint: 34/2019 [ARXIV] Green Open Access
A. Uschmajew and B.
Vandereycken:
Geometric methods on low-rank matrix and tensor manifolds.
Bibtex [PDF] Green Open Access
P.
Gelß ; S.
Matera ; R.
Schneider and A. Uschmajew:
Low-rank approximability of nearest neighbor interaction systems.
Bibtex MIS-Preprint: 82/2018 Green Open Access
A. Uschmajew and B.
Vandereycken:
On critical points of quadratic low-rank matrix optimization problems.
Bibtex MIS-Preprint: 58/2018 Green Open Access
A.
Phan ; A.
Cichocki ; A. Uschmajew ; P.
Tichavsky ; G.
Luta and D.
Mandic:
Tensor networks for latent variable analysis. Part I : Algorithms for tensor train
decomposition.
Bibtex [ARXIV] Green Open Access
Publications
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] Green Open Access
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]
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] Green 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] Gold 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] Green 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] Green 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] Gold 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] Gold 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] Green 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] Green 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] Green 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] Green 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] Green Open Access
R.
Schneider and A. Uschmajew:
Convergence results for projected line-search methods on varieties of low-rank matrices
via Lojasiewicz inequality.
SIAM journal on optimization,
25 (2016) 1, p. 622-646 Bibtex [DOI] [ARXIV] [PDF] Green 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] Green 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] Green 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] Green 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] Green 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] Green 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] Green 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] Green 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] Green 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]
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] Green Open Access
S.
R.
Chinnamsetty ; H.
Luo ; W.
Hackbusch ; H.
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] Green 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] Green Open Access
A. Uschmajew:
Regularity of tensor product approximations to square integrable functions.
Constructive approximation,
34 (2011) 3, p. 371-391 Bibtex [DOI] [PDF] Green 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]
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] Green Open Access