André Uschmajew
MaxPlanckInstitut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany
Office: G3 08
Contact:
Email
Phone:
+49 341 9959 824
Fax:
+49 341 9959 658
André Uschmajew
About
I am Max Planck Research Group Leader for the group Tensors and Optimization at MPI MiS in Leipzig.
My research is on lowrank approximation of matrices and tensors, multivariate functions, and highdimensional equations. I am particularly interested in the algebraic and geometric structures that underlie multilinear representations of lowrank matrix and tensor manifolds, and their implications on the applicability and convergence of numerical optimization methods.
Academic CV:
 since Oct. 2017: Max Planck Research Group Leader at MPI MiS, Leipzig, Germany
 2014  2017 Bonn Junior Fellow Professor at University of Bonn, Germany
 2013  2014 Postdoc at EPF Lausanne, Switzerland
 2008  2012 PhD at TU Berlin
I am an associate editor of Linear Algebra and Its Applications (LAA) and of Numerical Algebra, Control and Optimization (NACO).
I am a coinitiator of the Mathematics of Data Initiative at MPI MiS.
Activities
 The 2020 Annual GAMM AG Workshop Computational and Mathematical Methods in Data Science (COMinDS 2020), September 10  11, is coorganized by Max von Renesse (Leipzig University) and myself. It now takes place virtually!
 With Roland Herzog (TU Chemnitz) we are organizing a minisymposium on Optimization on manifolds: theory and numerics at the DMV Annual Meeting 2020 in Chemnitz, September 14  18, which takes place online.

Past international workshops:
Lowrank Optimization and Applications 2019, April 01  05, 2019, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Nonsmooth Optimization and its Applications, May 15  19, 2017, Hausdorff Center for Mathematics, University of Bonn, Germany
Lowrank Optimization and Applications 2015, June 08  12, 2015, Hausdorff Center for Mathematics, University of Bonn, Germany
Publications
Preprints
M. Bachmayr ; H. Eisenmann ; E. Kieri and A. Uschmajew: Existence of dynamical lowrank approximations to parabolic problems. Bibtex MISPreprint: 33/2020 [ARXIV] Repository Open Access
W. Hackbusch and A. Uschmajew: Modified iterations for datasparse solution of linear systems. Bibtex MISPreprint: 58/2020 Repository Open Access
C. Krumnow ; M. Pfeffer and A. Uschmajew: Computing eigenspaces with low rank constraints. Bibtex MISPreprint: 102/2019 Repository Open Access
P. Gelß ; S. Matera ; R. Schneider and A. Uschmajew: Lowrank approximability of nearest neighbor interaction systems. Bibtex MISPreprint: 82/2018 Repository Open Access
Book chapter
A. Uschmajew and B. Vandereycken: Geometric methods on lowrank matrix and tensor manifolds. Handbook of variational methods for nonlinear geometric data / P. Grohs... (eds.). Springer, 2020.  P. 261313 Bibtex [DOI] [PDF] Journal Open Access
Edited volume
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 1519, 2017. Springer Birkhäuser, 2019.  VII, 149 p. (International series of numerical mathematics ; 170) ISBN 9783030113698 Bibtex [DOI]
Journal articles and proceedings
A. Agrachev ; K. Kozhasov and A. Uschmajew: Chebyshev polynomials and best rankone approximation ratio. SIAM journal on matrix analysis and applications, 41 (2020) 1, p. 308331 Bibtex MISPreprint: 34/2019 [DOI] [ARXIV] Repository Open Access
A. 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, Vol. not yet known, pp. not yet known Bibtex [DOI] [ARXIV] Repository Open Access
A. Uschmajew and B. Vandereycken: On critical points of quadratic lowrank matrix optimization problems. IMA journal of numerical analysis, Vol. not yet known, pp. not yet known Bibtex MISPreprint: 58/2018 [DOI] Journal Open Access
S. Hosseini ; D. R. Luke and A. Uschmajew: Tangent and normal cones for lowrank matrices. Nonsmooth optimization and its applications / S. Hosseini... (eds.). Springer Birkhäuser, 2019.  P. 4553 (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 lowrank optimization. SIAM journal on optimization, 29 (2019) 4, p. 28532880 Bibtex [DOI] [PDF] Repository Open Access
M. Pfeffer ; A. Uschmajew ; A. Amaro and U. Pfeffer: Data fusion techniques for the integration of multidomain genomic data from uveal melanoma. Cancers, 11 (2019) 10, 1434 Bibtex MISPreprint: 42/2019 [DOI] Journal Open Access
Z. Li ; Y. Nakatsukasa ; T. Soma and A. Uschmajew: On orthogonal tensors and best rankone approximation ratio. SIAM journal on matrix analysis and applications, 39 (2018) 1, p. 400425 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. 34593479 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
W. Hackbusch ; D. Kressner and A. Uschmajew: Perturbation of higherorder singular values. SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 374387 Bibtex MISPreprint: 51/2016 [DOI] [PDF] Journal Open Access
W. Hackbusch and A. Uschmajew: On the interconnection between the higherorder singular values of real tensors. Numerische Mathematik, 135 (2017) 3, p. 875894 Bibtex MISPreprint: 62/2015 [DOI] Journal 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. 173189 Bibtex [DOI] [PDF] Repository Open Access
Y. Nakatsukasa ; T. Soma and A. Uschmajew: Finding a lowrank basis in a matrix subspace. Mathematical programming, 162 (2017) 12, p. 325361 Bibtex [DOI] [ARXIV] Repository Open Access
M. Bachmayr ; R. Schneider and A. Uschmajew: Tensor networks and hierarchical tensors for the solution of highdimensional partial differential equations. Foundations of computational mathematics, 16 (2016) 6, p. 14231472 Bibtex [DOI] [PDF] Repository Open Access
L. Karlsson ; D. Kressner and A. Uschmajew: Parallel algorithms for tensor completion in the CP format. Parallel computing, 57 (2016), p. 222234 Bibtex [DOI] [PDF] Repository Open Access
D. Kressner and A. Uschmajew: On lowrank approximability of solutions to highdimensional operator equations and eigenvalue problems. Linear algebra and its applications, 493 (2016), p. 556572 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
R. Schneider and A. Uschmajew: Convergence results for projected linesearch methods on varieties of lowrank matrices via Łojasiewicz inequality. SIAM journal on optimization, 25 (2016) 1, p. 622646 Bibtex [DOI] [ARXIV] [PDF] Repository 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. 210233 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew: A new convergence proof for the higherorder power method and generalizations. Pacific journal of optimization : an international journal, 11 (2015) 2, p. 309321 Bibtex [ARXIV] [FREELINK] [PDF] Repository Open Access
A. Uschmajew: Some results concerning rankone truncated steepest descent directions in tensor spaces. 2015 International conference on sampling theory and applications (SampTA) took place May 2529, 2015 in Washington, DC, USA IEEE, 2015.  P. 415419 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew and B. Vandereycken: Greedy rank updates combined with Riemannian descent methods for lowrank optimization. 2015 International conference on sampling theory and applications (SampTA) took place May 2529, 2015 in Washington, DC, USA IEEE, 2015.  P. 420424 Bibtex [DOI] [PDF] Repository Open Access
D. Kressner ; M. Steinlechner and A. Uschmajew: Lowrank tensor methods with subspace correction for symmetric eigenvalue problems. SIAM journal on scientific computing, 36 (2014) 5, p. A2346A2368 Bibtex [DOI] [PDF] Repository 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. 5671 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew and B. Vandereycken: Linesearch methods and rank increase on lowrank matrix varieties. 2014 International symposium on nonlinear theory and its applications : NOLTA2014, Luzern, Switzerland, September 1418, 2014 IEICE, 2014.  P. 5255 Bibtex [FREELINK] [PDF] Repository 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. 11341162 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew ; D. Kressner and M. Steinlechner: Lowrank 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. 32963298 Bibtex [DOI]
A. Uschmajew and B. Vandereycken: The geometry of algorithms using hierarchical tensors. Linear algebra and its applications, 439 (2013) 1, p. 133166 Bibtex [DOI] [PDF] Repository Open Access
S. R. Chinnamsetty ; H. Luo ; W. Hackbusch ; H. Flad and A. Uschmajew: Bridging the gap between quantum Monte Carlo and F12methods. Chemical physics, 401 (2012), p. 3644 Bibtex MISPreprint: 68/2011 [DOI] [PDF] Repository 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. 639652 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew: Regularity of tensor product approximations to square integrable functions. Constructive approximation, 34 (2011) 3, p. 371391 Bibtex [DOI] [PDF] Repository Open Access
A. Uschmajew: The regularity of tensor product approximations in \(L^2\) in dependence of the target function [In: Mathematical methods in quantum chemistry ; June 26 th  July 2nd, 2011 ; report no. 32/2011]. Oberwolfach reports, 8 (2011) 2, p. 18021804 Bibtex [DOI]
A. Uschmajew: Wellposedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations. Numerische Mathematik, 115 (2010) 2, p. 309331 Bibtex [DOI] [PDF] Repository Open Access