Bellon, Antonio; Dressler, Mareike; Kungurtsev, Vyacheslav; Mareček, Jakub; Uschmajew, André Time-varying semidefinite programming: path following a Burer-Monteiro factorization. (English) Zbl 07790167 SIAM J. Optim. 34, No. 1, 1-26 (2024). MSC: 90C22 90C30 90C31 49M15 PDFBibTeX XMLCite \textit{A. Bellon} et al., SIAM J. Optim. 34, No. 1, 1--26 (2024; Zbl 07790167) Full Text: DOI arXiv
Dressler, Mareike; Uschmajew, André; Chandrasekaran, Venkat Kronecker product approximation of operators in spectral norm via alternating SDP. (English) Zbl 07765797 SIAM J. Matrix Anal. Appl. 44, No. 4, 1693-1708 (2023). MSC: 47A58 90C22 65F45 PDFBibTeX XMLCite \textit{M. Dressler} et al., SIAM J. Matrix Anal. Appl. 44, No. 4, 1693--1708 (2023; Zbl 07765797) Full Text: DOI arXiv
Oseledets, Ivan V.; Rakhuba, Maxim V.; Uschmajew, André Local convergence of alternating low-rank optimization methods with overrelaxation. (English) Zbl 07729584 Numer. Linear Algebra Appl. 30, No. 3, e2459, 15 p. (2023). MSC: 65F55 65F10 PDFBibTeX XMLCite \textit{I. V. Oseledets} et al., Numer. Linear Algebra Appl. 30, No. 3, e2459, 15 p. (2023; Zbl 07729584) Full Text: DOI arXiv
Eisenmann, Henrik; Krahmer, Felix; Pfeffer, Max; Uschmajew, André Riemannian thresholding methods for row-sparse and low-rank matrix recovery. (English) Zbl 1522.65067 Numer. Algorithms 93, No. 2, 669-693 (2023). MSC: 65F55 65K99 PDFBibTeX XMLCite \textit{H. Eisenmann} et al., Numer. Algorithms 93, No. 2, 669--693 (2023; Zbl 1522.65067) Full Text: DOI arXiv
Eisenmann, Henrik; Uschmajew, André Maximum relative distance between real rank-two and rank-one tensors. (English) Zbl 1514.15034 Ann. Mat. Pura Appl. (4) 202, No. 2, 993-1009 (2023). MSC: 15A69 15A60 14N07 26C05 PDFBibTeX XMLCite \textit{H. Eisenmann} and \textit{A. Uschmajew}, Ann. Mat. Pura Appl. (4) 202, No. 2, 993--1009 (2023; Zbl 1514.15034) Full Text: DOI arXiv
Bachmayr, Markus; Eisenmann, Henrik; Uschmajew, André Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. arXiv:2308.16720 Preprint, arXiv:2308.16720 [math.NA] (2023). MSC: 35K15 35R01 15A69 65M12 BibTeX Cite \textit{M. Bachmayr} et al., ``Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations'', Preprint, arXiv:2308.16720 [math.NA] (2023) Full Text: arXiv OA License
Olikier, Guillaume; Uschmajew, André; Vandereycken, Bart Gauss-Southwell type descent methods for low-rank matrix optimization. arXiv:2306.00897 Preprint, arXiv:2306.00897 [math.OC] (2023). BibTeX Cite \textit{G. Olikier} et al., ``Gauss-Southwell type descent methods for low-rank matrix optimization'', Preprint, arXiv:2306.00897 [math.OC] (2023) Full Text: arXiv OA License
Kressner, Daniel; Ni, Tingting; Uschmajew, André On the approximation of vector-valued functions by samples. arXiv:2304.03212 Preprint, arXiv:2304.03212 [math.NA] (2023). BibTeX Cite \textit{D. Kressner} et al., ``On the approximation of vector-valued functions by samples'', Preprint, arXiv:2304.03212 [math.NA] (2023) Full Text: arXiv OA License
Uschmajew, André; Zeiser, Andreas Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary. arXiv:2303.01856 Preprint, arXiv:2303.01856 [math.NA] (2023). BibTeX Cite \textit{A. Uschmajew} and \textit{A. Zeiser}, ``Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary'', Preprint, arXiv:2303.01856 [math.NA] (2023) Full Text: arXiv OA License
Lehmann, Tobias; von Renesse, Max-K.; Sambale, Alexander; Uschmajew, André A note on overrelaxation in the Sinkhorn algorithm. (English) Zbl 1503.90070 Optim. Lett. 16, No. 8, 2209-2220 (2022). MSC: 90C08 PDFBibTeX XMLCite \textit{T. Lehmann} et al., Optim. Lett. 16, No. 8, 2209--2220 (2022; Zbl 1503.90070) Full Text: DOI arXiv
Uschmajew, André; Vandereycken, Bart A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions. (English) Zbl 1489.90128 J. Optim. Theory Appl. 194, No. 1, 364-373 (2022). MSC: 90C25 65K05 PDFBibTeX XMLCite \textit{A. Uschmajew} and \textit{B. Vandereycken}, J. Optim. Theory Appl. 194, No. 1, 364--373 (2022; Zbl 1489.90128) Full Text: DOI arXiv
Hackbusch, Wolfgang; Uschmajew, André Modified iterations for data-sparse solution of linear systems. (English) Zbl 1472.65037 Vietnam J. Math. 49, No. 2, 493-512 (2021). MSC: 65F10 65J99 41A46 PDFBibTeX XMLCite \textit{W. Hackbusch} and \textit{A. Uschmajew}, Vietnam J. Math. 49, No. 2, 493--512 (2021; Zbl 1472.65037) Full Text: DOI
Bachmayr, Markus; Eisenmann, Henrik; Kieri, Emil; Uschmajew, André Existence of dynamical low-rank approximations to parabolic problems. (English) Zbl 1482.65136 Math. Comput. 90, No. 330, 1799-1830 (2021). MSC: 65M06 65F55 65L05 35K15 35R01 15A18 15A69 35A01 35A02 35D30 PDFBibTeX XMLCite \textit{M. Bachmayr} et al., Math. Comput. 90, No. 330, 1799--1830 (2021; Zbl 1482.65136) Full Text: DOI arXiv
Krumnow, Christian; Pfeffer, Max; Uschmajew, André Computing eigenspaces with low rank constraints. (English) Zbl 1462.65039 SIAM J. Sci. Comput. 43, No. 1, A586-A608 (2021). MSC: 65F15 65K10 53B21 15A18 15A69 PDFBibTeX XMLCite \textit{C. Krumnow} et al., SIAM J. Sci. Comput. 43, No. 1, A586--A608 (2021; Zbl 1462.65039) Full Text: DOI
Uschmajew, André; Vandereycken, Bart On critical points of quadratic low-rank matrix optimization problems. (English) Zbl 1464.65042 IMA J. Numer. Anal. 40, No. 4, 2626-2651 (2020). MSC: 65F55 PDFBibTeX XMLCite \textit{A. Uschmajew} and \textit{B. Vandereycken}, IMA J. Numer. Anal. 40, No. 4, 2626--2651 (2020; Zbl 1464.65042) Full Text: DOI
Uschmajew, André; Vandereycken, Bart Geometric methods on low-rank matrix and tensor manifolds. (English) Zbl 1512.65078 Grohs, Philipp (ed.) et al., Handbook of variational methods for nonlinear geometric data. Cham: Springer. 261-313 (2020). MSC: 65F55 15A69 53B21 90C30 90C48 PDFBibTeX XMLCite \textit{A. Uschmajew} and \textit{B. Vandereycken}, in: Handbook of variational methods for nonlinear geometric data. Cham: Springer. 261--313 (2020; Zbl 1512.65078) Full Text: DOI
Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André Chebyshev polynomials and best rank-one approximation ratio. (English) Zbl 1435.15019 SIAM J. Matrix Anal. Appl. 41, No. 1, 308-331 (2020). MSC: 15A69 15A60 14P25 26C05 PDFBibTeX XMLCite \textit{A. Agrachev} et al., SIAM J. Matrix Anal. Appl. 41, No. 1, 308--331 (2020; Zbl 1435.15019) Full Text: DOI arXiv
Hosseini, Seyedehsomayeh; Uschmajew, André A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization. (English) Zbl 1428.49015 SIAM J. Optim. 29, No. 4, 2853-2880 (2019). MSC: 49J52 65K05 14P05 15A99 49J53 PDFBibTeX XMLCite \textit{S. Hosseini} and \textit{A. Uschmajew}, SIAM J. Optim. 29, No. 4, 2853--2880 (2019; Zbl 1428.49015) Full Text: DOI
Hosseini, Seyedehsomayeh; Luke, D. Russell; Uschmajew, André Tangent and normal cones for low-rank matrices. (English) Zbl 1417.15050 Hosseini, Seyedehsomayeh (ed.) et al., Nonsmooth optimization and its applications. Based on the workshop “Nonsmooth Optimization and its Applications”, Bonn, Germany, May 15–19, 2017. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 170, 45-53 (2019). MSC: 15B48 65K10 90C30 PDFBibTeX XMLCite \textit{S. Hosseini} et al., ISNM, Int. Ser. Numer. Math. 170, 45--53 (2019; Zbl 1417.15050) Full Text: DOI
Hosseini, Seyedehsomayeh (ed.); Mordukhovich, Boris S. (ed.); Uschmajew, André (ed.) Nonsmooth optimization and its applications. Based on the workshop “Nonsmooth Optimization and its Applications”, Bonn, Germany, May 15–19, 2017. (English) Zbl 1417.49001 ISNM. International Series of Numerical Mathematics 170. Cham: Birkhäuser (ISBN 978-3-030-11369-8/hbk; 978-3-030-11370-4/ebook). vii, 149 p. (2019). MSC: 49-06 90-06 49J52 90C56 90C25 00B25 PDFBibTeX XMLCite \textit{S. Hosseini} (ed.) et al., Nonsmooth optimization and its applications. Based on the workshop ``Nonsmooth Optimization and its Applications'', Bonn, Germany, May 15--19, 2017. Cham: Birkhäuser (2019; Zbl 1417.49001) Full Text: DOI
Oseledets, Ivan V.; Rakhuba, Maxim V.; Uschmajew, André Alternating least squares as moving subspace correction. (English) Zbl 1417.65134 SIAM J. Numer. Anal. 56, No. 6, 3459-3479 (2018). MSC: 65K05 65F10 65F30 15A69 PDFBibTeX XMLCite \textit{I. V. Oseledets} et al., SIAM J. Numer. Anal. 56, No. 6, 3459--3479 (2018; Zbl 1417.65134) Full Text: DOI arXiv
Li, Zhening; Nakatsukasa, Yuji; Soma, Tasuku; Uschmajew, André On orthogonal tensors and best rank-one approximation ratio. (English) Zbl 1390.15081 SIAM J. Matrix Anal. Appl. 39, No. 1, 400-425 (2018). MSC: 15A69 15A60 17A75 PDFBibTeX XMLCite \textit{Z. Li} et al., SIAM J. Matrix Anal. Appl. 39, No. 1, 400--425 (2018; Zbl 1390.15081) Full Text: DOI arXiv
Hackbusch, Wolfgang; Kressner, Daniel; Uschmajew, André Perturbation of higher-order singular values. (English) Zbl 1371.15011 SIAM J. Appl. Algebra Geom. 1, No. 1, 374-387 (2017). MSC: 15A18 15A69 65F20 PDFBibTeX XMLCite \textit{W. Hackbusch} et al., SIAM J. Appl. Algebra Geom. 1, No. 1, 374--387 (2017; Zbl 1371.15011) Full Text: DOI
Nakatsukasa, Yuji; Soma, Tasuku; Uschmajew, André Finding a low-rank basis in a matrix subspace. (English) Zbl 1358.90107 Math. Program. 162, No. 1-2 (A), 325-361 (2017). MSC: 90C26 PDFBibTeX XMLCite \textit{Y. Nakatsukasa} et al., Math. Program. 162, No. 1--2 (A), 325--361 (2017; Zbl 1358.90107) Full Text: DOI arXiv
Hackbusch, Wolfgang; Uschmajew, André On the interconnection between the higher-order singular values of real tensors. (English) Zbl 1364.15018 Numer. Math. 135, No. 3, 875-894 (2017). Reviewer: John D. Dixon (Ottawa) MSC: 15A69 15A18 15A21 PDFBibTeX XMLCite \textit{W. Hackbusch} and \textit{A. Uschmajew}, Numer. Math. 135, No. 3, 875--894 (2017; Zbl 1364.15018) Full Text: DOI
Hosseini, Seyedehsomayeh; Uschmajew, André A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds. (English) Zbl 1357.49062 SIAM J. Optim. 27, No. 1, 173-189 (2017). MSC: 49J52 65K05 58C05 PDFBibTeX XMLCite \textit{S. Hosseini} and \textit{A. Uschmajew}, SIAM J. Optim. 27, No. 1, 173--189 (2017; Zbl 1357.49062) Full Text: DOI
Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. (English) Zbl 1357.65153 Found. Comput. Math. 16, No. 6, 1423-1472 (2016). MSC: 65M22 35Q84 35Q40 35Q55 PDFBibTeX XMLCite \textit{M. Bachmayr} et al., Found. Comput. Math. 16, No. 6, 1423--1472 (2016; Zbl 1357.65153) Full Text: DOI Link
Kressner, Daniel; Uschmajew, André On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems. (English) Zbl 1336.65093 Linear Algebra Appl. 493, 556-572 (2016). MSC: 65J10 15A69 41A25 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{A. Uschmajew}, Linear Algebra Appl. 493, 556--572 (2016; Zbl 1336.65093) Full Text: DOI arXiv
Phan, Anh-Huy; Cichocki, Andrzej; Uschmajew, Andre; Tichavsky, Petr; Luta, George; Mandic, Danilo Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition. arXiv:1609.09230 Preprint, arXiv:1609.09230 [cs.NA] (2016). BibTeX Cite \textit{A.-H. Phan} et al., ``Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition'', Preprint, arXiv:1609.09230 [cs.NA] (2016) Full Text: arXiv OA License
Schneider, Reinhold; Uschmajew, André Convergence results for projected line-search methods on varieties of low-rank matrices via Łojasiewicz inequality. (English) Zbl 1355.65079 SIAM J. Optim. 25, No. 1, 622-646 (2015). MSC: 65K05 90C30 90C48 PDFBibTeX XMLCite \textit{R. Schneider} and \textit{A. Uschmajew}, SIAM J. Optim. 25, No. 1, 622--646 (2015; Zbl 1355.65079) Full Text: DOI arXiv
Li, Zhening; Uschmajew, André; Zhang, Shuzhong On convergence of the maximum block improvement method. (English) Zbl 1355.65077 SIAM J. Optim. 25, No. 1, 210-233 (2015). MSC: 65K05 90C26 PDFBibTeX XMLCite \textit{Z. Li} et al., SIAM J. Optim. 25, No. 1, 210--233 (2015; Zbl 1355.65077) Full Text: DOI Link
Uschmajew, André A new convergence proof for the higher-order power method and generalizations. (English) Zbl 1339.65054 Pac. J. Optim. 11, No. 2, 309-321 (2015). Reviewer: Vasilis Dimitriou (Chania) MSC: 65F15 15A69 65K05 90C26 65F20 PDFBibTeX XMLCite \textit{A. Uschmajew}, Pac. J. Optim. 11, No. 2, 309--321 (2015; Zbl 1339.65054) Full Text: arXiv Link
Kressner, Daniel; Steinlechner, Michael; Uschmajew, André Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. (English) Zbl 1307.65040 SIAM J. Sci. Comput. 36, No. 5, A2346-A2368 (2014). MSC: 65F15 65N25 65F08 PDFBibTeX XMLCite \textit{D. Kressner} et al., SIAM J. Sci. Comput. 36, No. 5, A2346--A2368 (2014; Zbl 1307.65040) Full Text: DOI
Schneider, Reinhold; Uschmajew, André Approximation rates for the hierarchical tensor format in periodic Sobolev spaces. (English) Zbl 1329.41033 J. Complexity 30, No. 2, 56-71 (2014). MSC: 41A46 41A63 46E30 PDFBibTeX XMLCite \textit{R. Schneider} and \textit{A. Uschmajew}, J. Complexity 30, No. 2, 56--71 (2014; Zbl 1329.41033) Full Text: DOI
Uschmajew, André; Vandereycken, Bart The geometry of algorithms using hierarchical tensors. (English) Zbl 1281.65062 Linear Algebra Appl. 439, No. 1, 133-166 (2013). MSC: 65F15 15A69 65F20 PDFBibTeX XMLCite \textit{A. Uschmajew} and \textit{B. Vandereycken}, Linear Algebra Appl. 439, No. 1, 133--166 (2013; Zbl 1281.65062) Full Text: DOI
Rohwedder, Thorsten; Uschmajew, André On local convergence of alternating schemes for optimization of convex problems in the tensor train format. (English) Zbl 1273.65088 SIAM J. Numer. Anal. 51, No. 2, 1134-1162 (2013). Reviewer: Hans Benker (Merseburg) MSC: 65K10 90C25 PDFBibTeX XMLCite \textit{T. Rohwedder} and \textit{A. Uschmajew}, SIAM J. Numer. Anal. 51, No. 2, 1134--1162 (2013; Zbl 1273.65088) Full Text: DOI Link
Uschmajew, André Local convergence of the alternating least squares algorithm for canonical tensor approximation. (English) Zbl 1252.65085 SIAM J. Matrix Anal. Appl. 33, No. 2, 639-652 (2012). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 15A69 65K10 65F10 PDFBibTeX XMLCite \textit{A. Uschmajew}, SIAM J. Matrix Anal. Appl. 33, No. 2, 639--652 (2012; Zbl 1252.65085) Full Text: DOI
Uschmajew, André Regularity of tensor product approximations to square integrable functions. (English) Zbl 1237.41010 Constr. Approx. 34, No. 3, 371-391 (2011). Reviewer: Yuri A. Farkov (Moscow) MSC: 41A46 15A69 49N60 PDFBibTeX XMLCite \textit{A. Uschmajew}, Constr. Approx. 34, No. 3, 371--391 (2011; Zbl 1237.41010) Full Text: DOI
Uschmajew, André Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations. (English) Zbl 1192.65086 Numer. Math. 115, No. 2, 309-331 (2010). Reviewer: Berwin A. Turlach (Crawley) MSC: 65K05 90C25 PDFBibTeX XMLCite \textit{A. Uschmajew}, Numer. Math. 115, No. 2, 309--331 (2010; Zbl 1192.65086) Full Text: DOI