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, 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

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

T. Brysiewicz and F. Gesmundo: The degree of Stiefel manifolds. Enumerative combinatorics and applications, 1 (2021) 3, S2R20 Bibtex [DOI] [ARXIV] 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
29.06.2022, 05:47