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Former Research Group

Tensors and Optimization - Publications

Explore the scholarly works of the "Tensors and Optimization" group. Browse journal articles, contributions in books and conference proceedings, academic theses, or discover our research through preprints.

inJournal
2023 Repository Open Access
Alessandra Bernardi, Claudia De Lazzari and Fulvio Gesmundo

Dimension of tensor network varieties

In: Communications in contemporary mathematics, 25 (2023) 10, p. 2250059
BibTex DOI: 10.1142/S0219199722500596 ArXiv: 2101.03148 MiS Preprint
inJournal
2023 Repository Open Access
Paul Breiding, Fulvio Gesmundo, Mateusz Michałek and Nick Vannieuwenhoven

Algebraic compressed sensing

In: Applied and computational harmonic analysis, 65 (2023), pp. 374-406
BibTex DOI: 10.1016/j.acha.2023.03.006 ArXiv: 2108.13208
inJournal
2023 Repository Open Access
Mareike Dressler, André Uschmajew and Venkat Chandrasekaran

Kronecker product approximation of operators in spectral norm via alternating SDP

In: SIAM journal on matrix analysis and applications, 44 (2023) 4, pp. 1693-1708
BibTex DOI: 10.1137/22M1509953 ArXiv: 2207.03186 MiS Preprint
inJournal
2023 Journal Open Access
Henrik Eisenmann and André Uschmajew

Maximum relative distance between real rank-two and rank-one tensors

In: Annali di matematica pura ed applicata, 202 (2023) 2, pp. 993-1009
BibTex DOI: 10.1007/s10231-022-01268-w ArXiv: 2111.12611 MiS Preprint
inJournal
2023 Journal Open Access
Henrik Eisenmann, Felix Krahmer, Max Pfeffer and André Uschmajew

Riemannian thresholding methods for row-sparse and low-rank matrix recovery

In: Numerical algorithms, 93 (2023) 2, pp. 669-693
BibTex DOI: 10.1007/s11075-022-01433-5 ArXiv: 2103.02356 MiS Preprint
inJournal
2023 Journal Open Access
Ivan V. Oseledets, Maxim Rakhuba and André Uschmajew

Local convergence of alternating low-rank optimization methods with overrelaxation

In: Numerical linear algebra with applications, 30 (2023) 3, e2459
BibTex DOI: 10.1002/nla.2459 ArXiv: 2111.14758 MiS Preprint
inJournal
2022 Journal Open Access
Arthur Bik and Henrik Eisenmann

The geometries of Jordan nets and Jordan webs

In: Annali di matematica pura ed applicata, 201 (2022) 5, pp. 2413-2464
BibTex DOI: 10.1007/s10231-022-01204-y ArXiv: 2201.04403 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2022 Journal Open Access
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg and Emanuele Ventura

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

In: Computational complexity, 31 (2022) 1, p. 1
BibTex DOI: 10.1007/s00037-021-00217-y ArXiv: 1909.04785
inJournal
2022 Journal Open Access
Edoardo Di Napoli, Paolo Bientinesi, Jiajia Li and André Uschmajew

Editorial : High-performance tensor computations in scientific computing and data science

In: Frontiers in applied mathematics and statistics, 8 (2022), p. 1038885
BibTex DOI: 10.3389/fams.2022.1038885
Academic
2022 Repository Open Access
Henrik Eisenmann

Multilinear optimization in low-rank models

Dissertation, Universität Leipzig, 2022
BibTex Link: nbn-resolving.org
inJournal
2022 Journal Open Access
Henrik Eisenmann and Yuji Nakatsukasa

Solving two-parameter eigenvalue problems using an alternating method

In: Linear algebra and its applications, 643 (2022), pp. 137-160
BibTex DOI: 10.1016/j.laa.2022.02.024 ArXiv: 2008.03385 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2022 Journal Open Access
Fulvio Gesmundo and Chiara Meroni

The geometry of discotopes

In: Le Matematiche, 77 (2022) 1, pp. 143-171
BibTex ArXiv: 2111.01241 Link: lematematiche.dmi.unict.it
inJournal
2022 Journal Open Access
Tobias Lehmann, Max von Renesse, Alexander Sambale and André Uschmajew

A note on overrelaxation in the Sinkhorn algorithm

In: Optimization letters, 16 (2022) 8, pp. 2209-2220
BibTex DOI: 10.1007/s11590-021-01830-0 ArXiv: 2012.12562 MiS Preprint
inJournal
2022 Journal Open Access
André Uschmajew and Bart Vandereycken

A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions

In: Journal of optimization theory and applications, 194 (2022) 1, pp. 364-373
BibTex DOI: 10.1007/s10957-022-02032-z ArXiv: 2106.08020 MiS Preprint
inJournal
2021 Repository Open Access
Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew

Existence of dynamical low-rank approximations to parabolic problems

In: Mathematics of computation, 90 (2021) 330, pp. 1799-1830
BibTex DOI: 10.1090/mcom/3626 ArXiv: 2002.12197 MiS Preprint
inJournal
2021 Journal Open Access
Arthur Bik, Henrik Eisenmann and Bernd Sturmfels

Jordan algebras of symmetric matrices

In: Le Matematiche, 76 (2021) 2, pp. 337-353
BibTex DOI: 10.4418/2021.76.2.3 ArXiv: 2010.00277 Code: mathrepo.mis.mpg.de
inJournal
2021 Journal Open Access
Taylor Brysiewicz and Fulvio Gesmundo

The degree of Stiefel manifolds

In: Enumerative combinatorics and applications, 1 (2021) 3, S2R20
BibTex DOI: 10.54550/eca2021v1s3r20 ArXiv: 1909.10085
inJournal
2021 Repository Open Access
Matthias Christandl, Fulvio Gesmundo, Mateusz Michałek and Jeroen Zuiddam

Border rank non-additivity for higher order tensors

In: SIAM journal on matrix analysis and applications, 42 (2021) 2, pp. 503-527
BibTex DOI: 10.1137/20M1357366 ArXiv: 2007.05458
inJournal
2021 Repository Open Access
Matthias Christandl, Fulvio Gesmundo, Daniel Stilck França and Albert H. Werner

Optimization at the boundary of the tensor network variety

In: Physical review / B, 103 (2021) 9, p. 195139
BibTex DOI: 10.1103/PhysRevB.103.195139 ArXiv: 2006.16963
inJournal
2021 Journal Open Access
Wolfgang Hackbusch and André Uschmajew

Modified iterations for data-sparse solution of linear systems

In: Vietnam journal of mathematics, 49 (2021) 2, pp. 493-512
BibTex DOI: 10.1007/s10013-021-00504-9 MiS Preprint
inJournal
2021 Repository Open Access
Christian Krumnow, Max Pfeffer and André Uschmajew

Computing eigenspaces with low rank constraints

In: SIAM journal on scientific computing, 43 (2021) 1, A586-A608
BibTex DOI: 10.1137/19M1308384 MiS Preprint
inJournal
2020 Repository Open Access
Andrei Agrachev, Khazhgali Kozhasov and André Uschmajew

Chebyshev polynomials and best rank-one approximation ratio

In: SIAM journal on matrix analysis and applications, 41 (2020) 1, pp. 308-331
BibTex DOI: 10.1137/19M1269713 ArXiv: 1904.00488 MiS Preprint
inJournal
2020 Journal Open Access
Martin Eigel, Manuel Marschall, Max Pfeffer and Reinhold Schneider

Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

In: Numerische Mathematik, 145 (2020) 3, pp. 655-692
BibTex DOI: 10.1007/s00211-020-01123-1 ArXiv: 1811.00319 MiS Preprint
inJournal
2020 Repository Open Access
André Uschmajew, Markus Bachmayr, Henrik Eisenmann and Emil Kieri

Dynamical low-rank approximation for parabolic problems [In: Mini-workshop : computational optimization on manifolds ; 15 November - 21 November 2020 ; report no. 36/2020]

In: Oberwolfach reports, 17 (2020) 4, pp. 1800-1802
BibTex DOI: 10.4171/OWR/2020/36 Link: publications.mfo.de
inBook
2020 Journal Open Access
André Uschmajew and Bart Vandereycken

Geometric methods on low-rank matrix and tensor manifolds

In: Handbook of variational methods for nonlinear geometric data / Philipp Grohs... (eds.)
Cham : Springer, 2020. - pp. 261-313
BibTex DOI: 10.1007/978-3-030-31351-7_9
inJournal
2020 Journal Open Access
André Uschmajew and Bart Vandereycken

On critical points of quadratic low-rank matrix optimization problems

In: IMA journal of numerical analysis, 40 (2020) 4, pp. 2626-2651
BibTex DOI: 10.1093/imanum/drz061 MiS Preprint
inJournal
2019 Repository Open Access
Seyedehsomayeh Hosseini and André Uschmajew

A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization

In: SIAM journal on optimization, 29 (2019) 4, pp. 2853-2880
BibTex DOI: 10.1137/17M1153571
Book
2019
Seyedehsomayeh Hosseini, Boris S. Mordukhovich and André Uschmajew (Eds.)

Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization and its Applications', Bonn, Germany, May 15-19, 2017

Cham : Springer Birkhäuser, 2019. - vii, 149
(International series of numerical mathematics ; 170)
ISBN: 978-3-030-11369-8, ISBN: 978-3-030-11370-4, ISSN: 0373-3149
BibTex DOI: 10.1007/978-3-030-11370-4
inBook
2019 Repository Open Access
Seyedehsomayeh Hosseini, D. Russell Luke and André Uschmajew

Tangent and normal cones for low-rank matrices

In: Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization and its Applications', Bonn, Germany, May 15-19, 2017 / Seyedehsomayeh Hosseini... (eds.)
Cham : Springer Birkhäuser, 2019. - pp. 45-53
(International series of numerical mathematics ; 170)
BibTex DOI: 10.1007/978-3-030-11370-4_3 Link: neitzel.ins.uni-bonn.de
inJournal
2019 Journal Open Access
Max Pfeffer, André Uschmajew, Adriana Amaro and Ulrich Pfeffer

Data fusion techniques for the integration of multi-domain genomic data from uveal melanoma

In: Cancers, 11 (2019) 10, p. 1434
BibTex DOI: 10.3390/cancers11101434 MiS Preprint
inJournal
2019 Repository Open Access
Max Pfeffer, Anna Seigal and Bernd Sturmfels

Learning paths from signature tensors

In: SIAM journal on matrix analysis and applications, 40 (2019) 2, pp. 394-416
BibTex DOI: 10.1137/18M1212331 ArXiv: 1809.01588 MiS Preprint
inJournal
2018 Repository Open Access
Zhening Li, Yuji Nakatsukasa, Tasuku Soma and André Uschmajew

On orthogonal tensors and best rank-one approximation ratio

In: SIAM journal on matrix analysis and applications, 39 (2018) 1, pp. 400-425
BibTex DOI: 10.1137/17M1144349 ArXiv: 1707.02569
inJournal
2018 Repository Open Access
Ivan V. Oseledets, Maxim Rakhuba and André Uschmajew

Alternating least squares as moving subspace correction

In: SIAM journal on numerical analysis, 56 (2018) 6, pp. 3459-3479
BibTex DOI: 10.1137/17M1148712 ArXiv: 1709.07286