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

M. Pfeffer ; A. Uschmajew ; A. Amaro and U. Pfeffer: Development of data fusion techniques for the integration of multi-domain genomic data from uveal melanoma. Bibtex MIS-Preprint: 42/2019 Green Open Access

A. Uschmajew and B. Vandereycken: Geometric methods on low-rank matrix andtensor 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

S. Hosseini and A. Uschmajew: A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization. Bibtex [PDF] 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 / 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. Springer Birkhäuser, 2019. - VII, 149 p. (International series of numerical mathematics ; 170) ISBN 978-3-030-11369-8 Bibtex [DOI]

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. 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

Thesis

A. Uschmajew: Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen. Dissertation, Technische Universität Berlin, 2013 Bibtex [DOI] Green Open Access
19.08.2019, 05:46