**André Uschmajew**

Max-Planck-Institut 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

## News & Activities

- I am a guest editor for a Research Topic on High-Performance Tensor Computations in Scientific Computing and Data Science in Frontiers in Applied Mathematics and Statistics. The submission deadline is November 1, 2021.

- Past events:

Workshop: Hierarchical Numerical Methods for PDEs, September 28-29, 2021 at MPI Leipzig

Mathematical Foundations and Algorithms for Tensor Computations, May 3 -7, 2021, at IPAM, Online

GAMM AG Workshop Computational and Mathematical Methods in Data Science (COMinDS 2020), September 10 - 11, 2020, Online

Low-rank 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

Low-rank Optimization and Applications 2015, June 08 - 12, 2015, Hausdorff Center for Mathematics, University of Bonn, Germany

## About

I am Max Planck Research Group Leader for the group Tensors and Optimization at MPI MiS in Leipzig.

My research is on low-rank approximation of matrices and tensors, multivariate functions, and high-dimensional equations. I am particularly interested in the algebraic and geometric structures that underlie multilinear representations of low-rank 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
- 2019 and 2020 Visiting professor at Leipzig University, 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 co-initiator of the Mathematics of Data Initiative at MPI MiS.

# Publications

### Preprints

*Riemannian thresholding methods for row-sparse and low-rank matrix recovery*. Bibtex MIS-Preprint: 4/2021 [ARXIV] Repository Open Access

*Maximum relative distance between symmetric rank-two and rank-one tensors*. Bibtex MIS-Preprint: 27/2021 [ARXIV] Repository Open Access

*Local convergence of alternating low-rank optimization methods with overrelaxation*. Bibtex MIS-Preprint: 29/2021 [ARXIV] Repository Open Access

### Books

*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]

### Journal articles and proceedings

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds*. SIAM journal on optimization, 27 (2017) 1, p. 173-189 Bibtex [DOI] [PDF] Repository Open Access

*Finding a low-rank basis in a matrix subspace*. Mathematical programming, 162 (2017) 1-2, p. 325-361 Bibtex [DOI] [ARXIV] Repository Open Access

*Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations*. Foundations of computational mathematics, 16 (2016) 6, p. 1423-1472 Bibtex [DOI] [PDF] Repository Open Access

*Parallel algorithms for tensor completion in the CP format*. Parallel computing, 57 (2016), p. 222-234 Bibtex [DOI] [PDF] Repository Open Access

*On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems*. Linear algebra and its applications, 493 (2016), p. 556-572 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access

*Convergence results for projected line-search methods on varieties of low-rank matrices via Łojasiewicz inequality*. SIAM journal on optimization, 25 (2016) 1, p. 622-646 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access

*On convergence of the maximum block improvement method*. SIAM journal on optimization, 25 (2015) 1, p. 210-233 Bibtex [DOI] [PDF] Repository Open Access

*A new convergence proof for the higher-order power method and generalizations*. Pacific journal of optimization : an international journal, 11 (2015) 2, p. 309-321 Bibtex [ARXIV] [FREELINK] [PDF] Repository Open Access

*Some results concerning rank-one truncated steepest descent directions in tensor spaces*. 2015 International conference on sampling theory and applications (SampTA) took place May 25-29, 2015 in Washington, DC, USA IEEE, 2015. - P. 415-419 Bibtex [DOI] [PDF] Repository Open Access

*Greedy rank updates combined with Riemannian descent methods for low-rank optimization*. 2015 International conference on sampling theory and applications (SampTA) took place May 25-29, 2015 in Washington, DC, USA IEEE, 2015. - P. 420-424 Bibtex [DOI] [PDF] Repository Open Access

*Low-rank tensor methods with subspace correction for symmetric eigenvalue problems*. SIAM journal on scientific computing, 36 (2014) 5, p. A2346-A2368 Bibtex [DOI] [PDF] Repository Open Access

*Approximation rates for the hierarchical tensor format in periodic Sobolev spaces*. Journal of complexity, 30 (2014) 2, p. 56-71 Bibtex [DOI] [PDF] Repository Open Access

*Line-search methods and rank increase on low-rank matrix varieties*. 2014 International symposium on nonlinear theory and its applications : NOLTA2014, Luzern, Switzerland, September 14-18, 2014 IEICE, 2014. - P. 52-55 Bibtex [FREELINK] [PDF] Repository Open Access

*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. 1134-1162 Bibtex [DOI] [PDF] Repository Open Access

*Low-rank 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. 3296-3298 Bibtex [DOI] [FREELINK] Repository Open Access

*The geometry of algorithms using hierarchical tensors*. Linear algebra and its applications, 439 (2013) 1, p. 133-166 Bibtex [DOI] [PDF] Repository Open Access

*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

*Local convergence of the alternating least squares algorithm for canonical tensor approximation*. SIAM journal on matrix analysis and applications, 33 (2012) 2, p. 639-652 Bibtex [DOI] [PDF] Repository Open Access

*Regularity of tensor product approximations to square integrable functions*. Constructive approximation, 34 (2011) 3, p. 371-391 Bibtex [DOI] [PDF] Repository Open Access

*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. 1802-1804 Bibtex [DOI] [FREELINK] Repository Open Access

*Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations*. Numerische Mathematik, 115 (2010) 2, p. 309-331 Bibtex [DOI] [PDF] Repository Open Access