Tensors and Optimization

Head:
André Uschmajew (Email)

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

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Institute publications of the group

Preprints

A. Bernardi ; C. De Lazzari and F. Gesmundo: Dimension of tensor network varieties. Bibtex MIS-Preprint: 1/2021 [ARXIV] Repository Open Access

P. Breiding ; F. Gesmundo ; M. Michałek and N. Vannieuwenhoven: Algebraic compressed sensing. Bibtex [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

F. Gesmundo and C. Meroni: The geometry of discotopes. Bibtex [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

M. Pfeffer and J. A. Samper: The cone of \(5\times 5\) completely positive matrices. Bibtex [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]

S. Dahlke ; W. Dahmen ; M. Griebel ; W. Hackbusch ; K. Ritter ; R. Schneider ; C. Schwab and H. Yserentant (eds.): Extraction of quantifiable information from complex systems. Springer, 2014. - XIX, 432 p. (Lecture notes in computational science and engineering ; 102) ISBN 978-3-319-08158-8 Bibtex [DOI]

Journal articles and proceedings

A. Bik and H. Eisenmann: The geometries of Jordan nets and Jordan webs. Annali di matematica pura ed applicata, Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 1/2022 [DOI] [ARXIV] [CODELINK] Journal Open Access

A. Conner ; F. Gesmundo ; J. M. Landsberg and E. Ventura: Rank and border rank of Kronecker powers of tensors and Strassen's laser method. Computational complexity, 31 (2022) 1, 1 Bibtex [DOI] [ARXIV] Journal Open Access

H. Eisenmann and Y. Nakatsukasa: Solving two-parameter eigenvalue problems using an alternating method. Linear algebra and its applications, 643 (2022), p. 137-160 Bibtex MIS-Preprint: 83/2020 [DOI] [ARXIV] [CODELINK] Journal 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, 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

A. Bik ; H. Eisenmann and B. Sturmfels: Jordan algebras of symmetric matrices. Le Matematiche, 76 (2021) 2, p. 337-353 Bibtex [DOI] [ARXIV] [CODELINK] Journal Open Access

M. Christandl ; F. Gesmundo ; M. Michałek and J. Zuiddam: Border rank non-additivity for higher order tensors. SIAM journal on matrix analysis and applications, 42 (2021) 2, p. 503-527 Bibtex [DOI] [ARXIV] Repository Open Access

M. Christandl ; F. Gesmundo ; D. Stilck França and A. H. Werner: Optimization at the boundary of the tensor network variety. Physical review / B, 103 (2021) 9, 195139 Bibtex [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

M. Eigel ; M. Marschall ; M. Pfeffer and R. Schneider: Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. Numerische Mathematik, 145 (2020) 3, p. 655-692 Bibtex MIS-Preprint: 47/2018 [DOI] [ARXIV] Journal 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. Seigal and B. Sturmfels: Learning paths from signature tensors. SIAM journal on matrix analysis and applications, 40 (2019) 2, p. 394-416 Bibtex MIS-Preprint: 78/2018 [DOI] [ARXIV] 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. Dahlke ; W. Dahmen ; M. Griebel ; W. Hackbusch ; K. Ritter ; R. Schneider ; C. Schwab and H. Yserentant: Foreword. Extraction of quantifiable information from complex systems / S. Dahlke... (eds.). Springer, 2014 (Lecture notes in computational science and engineering ; 102) Bibtex [DOI]

W. Hackbusch and R. Schneider: Tensor spaces and hierarchical tensor representations. Extraction of quantifiable information from complex systems / S. Dahlke... (eds.). Springer, 2014. - P. 237-261 (Lecture notes in computational science and engineering ; 102) Bibtex [DOI]

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

H.-J. Flad ; W. Hackbusch ; D. Kolb and R. Schneider: Wavelet approximation of correlated wave functions. I. Basics. The journal of chemical physics, 116 (2002) 22, p. 9641-9657 Bibtex MIS-Preprint: 89/2001 [DOI] Repository Open Access
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