Tensors and Optimization

Head:
André Uschmajew (Email)

Phone:
+49 (0) 341 - 9959 - 824

Fax:
+49 (0) 341 - 9959 - 585

Address:
Inselstr. 22
04103 Leipzig

Publications André Uschmajew

Journal Articles

Hackbusch, Wolfgang ; Kressner, Daniel and André Uschmajew: Perturbation of higher-order singular values
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 374-387
Bibtex MIS-Preprint: 51/2016 DOI: 10.1137/16M1089873

Hackbusch, Wolfgang and André Uschmajew: On the interconnection between the higher-order singular values of real tensors
In: Numerische Mathematik, 135 (2017) 3, p. 875-894
Bibtex MIS-Preprint: 62/2015 DOI: 10.1007/s00211-016-0819-9

Hosseini, Seyedehsomayeh and André Uschmajew: A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds
In: SIAM journal on optimization, 27 (2017) 1, p. 173-189
Bibtex DOI: 10.1137/16M1069298

Nakatsukasa, Yuji ; Soma, Tasuku and André Uschmajew: Finding a low-rank basis in a matrix subspace
In: Mathematical programming, 162 (2017) 1-2, p. 325-361
Bibtex DOI: 10.1007/s10107-016-1042-2 ARXIV: https://arxiv.org/abs/1503.08601

Bachmayr, Markus ; Schneider, Reinhold and André Uschmajew: Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
In: Foundations of computational mathematics, 16 (2016) 6, p. 1423-1472
Bibtex DOI: 10.1007/s10208-016-9317-9

Karlsson, Lars ; Kressner, Daniel and André Uschmajew: Parallel algorithms for tensor completion in the CP format
In: Parallel computing, 57 (2016), p. 222-234
Bibtex DOI: 10.1016/j.parco.2015.10.002

Kressner, Daniel and André Uschmajew: On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
In: Linear algebra and its applications, 493 (2016), p. 556-572
Bibtex DOI: 10.1016/j.laa.2015.12.016 ARXIV: https://arxiv.org/abs/1406.7026

Schneider, Reinhold and André Uschmajew: Convergence results for projected line-search methods on varieties of low-rank matrices via Lojasiewicz inequality
In: SIAM journal on optimization, 25 (2016) 1, p. 622-646
Bibtex DOI: 10.1137/140957822 ARXIV: https://arxiv.org/abs/1402.5284

Li, Zhening ; Uschmajew, André and Shuzhong Zhang: On convergence of the maximum block improvement method
In: SIAM journal on optimization, 25 (2015) 1, p. 210-233
Bibtex DOI: 10.1137/130939110

Uschmajew, André: A new convergence proof for the higher-order power method and generalizations
In: Pacific journal of optimization : an international journal, 11 (2015) 2, p. 309-321
Bibtex ARXIV: https://arxiv.org/abs/1407.4586 LINK: http://www.ybook.co.jp/online2/pjov11-2.html

Kressner, Daniel ; Steinlechner, Michael and André Uschmajew: Low-rank tensor methods with subspace correction for symmetric eigenvalue problems
In: SIAM journal on scientific computing, 36 (2014) 5, p. A2346-A2368
Bibtex DOI: 10.1137/130949919

Schneider, Reinhold and André Uschmajew: Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
In: Journal of complexity, 30 (2014) 2, p. 56-71
Bibtex DOI: 10.1016/j.jco.2013.10.001

Rohwedder, Thorsten and André Uschmajew: On local convergence of alternating schemes for optimization of convex problems in the tensor train format
In: SIAM journal on numerical analysis, 51 (2013) 2, p. 1134-1162
Bibtex DOI: 10.1137/110857520

Uschmajew, André ; Kressner, Daniel and Michael Steinlechner: Low-rank tensor methods with subspace correction for symmetric eigenvalue problems
In: Oberwolfach reports, 10 (2013) 4, p. 3296-3298
Bibtex DOI: 10.4171/OWR/2013/56

Uschmajew, André and Bart Vandereycken: The geometry of algorithms using hierarchical tensors
In: Linear algebra and its applications, 439 (2013) 1, p. 133-166
Bibtex DOI: 10.1016/j.laa.2013.03.016

Chinnamsetty, Sambasiva Rao ; Luo, Hongjun ; Hackbusch, Wolfgang ; Flad, Heinz-Jürgen and André Uschmajew: Bridging the gap between quantum Monte Carlo and F12-methods
In: Chemical physics, 401 (2012), p. 36-44
Bibtex MIS-Preprint: 68/2011 DOI: 10.1016/j.chemphys.2011.09.019

Uschmajew, André: Local convergence of the alternating least squares algorithm for canonical tensor approximation
In: SIAM journal on matrix analysis and applications, 33 (2012) 2, p. 639-652
Bibtex DOI: 10.1137/110843587

Uschmajew, André: Regularity of tensor product approximations to square integrable functions
In: Constructive approximation, 34 (2011) 3, p. 371-391
Bibtex DOI: 10.1007/s00365-010-9125-4

Uschmajew, André: The regularity of tensor product approximations in \(Ł^2\) in dependence of the target function
In: Oberwolfach reports, 8 (2011) 2, p. 1802-1804
Bibtex DOI: 10.4171/OWR/2011/32

Uschmajew, André: Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations
In: Numerische Mathematik, 115 (2010) 2, p. 309-331
Bibtex DOI: 10.1007/s00211-009-0276-9

Publications in Books and Conference Proceedings

Uschmajew, André: Some results concerning rank-one truncated steepest descent directions in tensor spaces
In: 2015 International conference on sampling theory and applications (SampTA) took place May 25-29, 2015 in Washington, DC, USA
Piscataway, NJ : IEEE, 2015. - P. 415-419
Bibtex DOI: 10.1109/SAMPTA.2015.7148924

Uschmajew, André and Bart Vandereycken: Greedy rank updates combined with Riemannian descent methods for low-rank optimization
In: 2015 International conference on sampling theory and applications (SampTA) took place May 25-29, 2015 in Washington, DC, USA
Piscataway, NJ : IEEE, 2015. - P. 420-424
Bibtex DOI: 10.1109/SAMPTA.2015.7148925

Uschmajew, André and Bart Vandereycken: Line-search methods and rank increase on low-rank matrix varieties
In: 2014 International symposium on nonlinear theory and its applications : NOLTA2014, Luzern, Switzerland, September 14-18, 2014
Tokyo : IEICE, 2014. - P. 52-55
Bibtex LINK: http://www.ieice.org/nolta/symposium/archive/2014/nolta14fullvol.pdf

Preprints

Li, Zhening ; Nakatsukasa, Yuji ; Soma, Tasuku and André Uschmajew: On orthogonal tensors and best rank-one approximation ratio

Hosseini, Seyedehsomayeh and André Uschmajew: A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization

Academic Theses

Uschmajew, André: Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen
Dissertation, Technische Universität Berlin, 2013
Bibtex DOI: 10.14279/depositonce-3474

Uschmajew, André: Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen
Dissertation, Technische Universität Berlin, 2013
Bibtex DOI: 10.14279/depositonce-3474
18.10.2017, 05:45