Research Group of Prof. Dr. A. Uschmajew
Institute for Numerical Simulation
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Group publications

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Preprints:

[1] S. Hosseini, W. Huang, and R. Yousefpour. Line search algorithms for locally Lipschitz functions on Riemannian manifolds. Nov. 2016. INS Preprint No. 1626.
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[2] S. Hosseini and A. Uschmajew. A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization. Oct. 2016. INS Preprint No. 1624. Extended and revised version, March 2017.
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[3] W. Hackbusch, D. Kressner, and A. Uschmajew. Perturbation of higher-order singular values. July 2016. INS Preprint No. 1616.
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[4] S. Hosseini. Convergence of nonsmooth descent methods via Kurdyka-Lojasiewicz inequality on Riemannian manifolds. Nov. 2015. INS Preprint No. 1523.
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Journal Papers:

[1] E. Ghahraei, S. Hosseini, and M. R. Pouryayevali. Pseudo-Jacobian and characterization of monotone vector fields on Riemannian manifolds. J. Convex Anal., 24(1), 2017.
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[2] W. Hackbusch and A. Uschmajew. On the interconnection between the higher-order singular values of real tensors. Numer. Math., 135(3):875-894, 2017.
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[3] S. Hosseini and A. Uschmajew. A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds. SIAM J. Optim., 27(1):173-189, 2017.
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[4] Y. Nakatsukasa, T. Soma, and A. Uschmajew. Finding a low-rank basis in a matrix subspace. Math. Program., 162(1-2, Ser. A):325-361, 2017.
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[5] M. Bachmayr, R. Schneider, and A. Uschmajew. Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Found. Comput. Math., 16(6):1423-1472, 2016.
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[6] B. Brumm and E. Kieri. A matrix-free Legendre spectral method for initial-boundary value problems. Electron. Trans. Numer. Anal., 45:283-304, 2016.
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[7] E. Ghahraei, S. Hosseini, and M. R. Pouryayevali. Pseudo-Jacobian and and global inversion of nonsmooth mappings on Riemannian manifolds. Nonlinear Anal., 130:229-240, 2016.
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[8] P. Grohs and S. Hosseini. Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds. IMA J. Numer. Anal., 36(3):1167-1192, 2016.
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[9] P. Grohs and S. Hosseini. ε-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds. Adv. Comput. Math., 42(2):333-360, 2016.
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[10] S. Hosseini. Characterization of lower semicontinuous convex functions on Riemannian manifolds. Set-Valued Var. Anal., 2016. In press.
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[11] S. Hosseini and M. R. Pouryayevali. Equilibria on L-retracts in Riemannian manifolds. Topol. Methods Nonlinear Anal., 47(2):579-592, 2016.
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[12] L. Karlsson, D. Kressner, and A. Uschmajew. Parallel algorithms for tensor completion in the CP format. Parallel Comput., 57:222-234, 2016.
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[13] E. Kieri, C. Lubich, and H. Walach. Discretized dynamical low-rank approximation in the presence of small singular values. SIAM J. Numer. Anal., 54:1020-1038, 2016.
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[14] D. Kressner and A. Uschmajew. On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems. Linear Algebra Appl., 493:556-572, 2016.
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[15] S. Hosseini. Optimality conditions for global minima of nonconvex functions on Riemannian manifolds. 2015. Accepted in Pac. J. Optim.
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[16] E. Kieri. Stiff convergence of force-gradient operator splitting methods. Appl. Numer. Math., 94:33-45, 2015.
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[17] E. Kieri, G. Kreiss, and O. Runborg. Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations. Adv. Appl. Math. Mech., 7:687-714, 2015.
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[18] Z. Li, A. Uschmajew, and S. Zhang. On convergence of the maximum block improvement method. SIAM J. Optim., 25(1):210-233, 2015.
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[19] M. Movahedi, D. Behmardi, and S. Hosseini. On the density theorem for the subdifferential of convex functions on Hadamard spaces. Pacific J. Math., 276(2):437-447, 2015.
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[20] R. Schneider and A. Uschmajew. Convergence results for projected line-search methods on varieties of low-rank matrices via Lojasiewicz inequality. SIAM J. Optim., 25(1):622-646, 2015.
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[21] A. Uschmajew. A new convergence proof for the higher-order power method and generalizations. Pac. J. Optim., 11(2):309-321, 2015.
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[22] E. Kieri. Accelerated convergence for Schrödinger equations with non-smooth potential. BIT, 54:729-748, 2014.
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[23] D. Kressner, M. Steinlechner, and A. Uschmajew. Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. SIAM J. Sci. Comput., 36(5):A2346-A2368, 2014.
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[24] R. Schneider and A. Uschmajew. Approximation rates for the hierarchical tensor format in periodic Sobolev spaces. J. Complexity, 30(2):56-71, 2014.
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[25] M. Alavi Hejazi, S. Hosseini, and M. R. Pouryayevali. On the calculus of limiting subjets on Riemannian manifolds. Mediterr. J. Math., 10(1):593-607, 2013.
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[26] A. Barani, S. Hosseini, and M. R. Pouryayevali. On the metric projection onto φ-convex subsets of Hadamard manifolds. Rev. Mat. Complut., 26(2):815-826, 2013.
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[27] J. H. Eschenburg and S. Hosseini. Symmetric spaces as Grassmannians. Manuscripta Math., 141(1-2):51-62, 2013.
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[28] S. Hosseini and M. R. Pouryayevali. Nonsmooth optimization techniques on Riemannian manifolds. J. Optim. Theory Appl., 158(2):328-342, 2013.
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[29] S. Hosseini and M. R. Pouryayevali. Euler characteristic of epi-Lipschitz subsets of Riemannian manifolds. J. Convex Anal., 20(1):67-91, 2013.
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[30] S. Hosseini and M. R. Pouryayevali. On the metric projection onto prox-regular subsets of Riemannian manifolds. Proc. Amer. Math. Soc., 141(1):233-244, 2013.
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[31] T. Rohwedder and A. Uschmajew. On local convergence of alternating schemes for optimization of convex problems in the tensor train format. SIAM J. Numer. Anal., 51(2):1134-1162, 2013.
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[32] A. Uschmajew and B. Vandereycken. The geometry of algorithms using hierarchical tensors. Linear Algebra Appl., 439(1):133-166, 2013.
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[33] S. R. Chinnamsetty, H. Luo, W. Hackbusch, H.-J. Flad, and A. Uschmajew. Bridging the gap between quantum Monte Carlo and F12-methods. Chem. Phys., 401:36-44, 2012.
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[34] E. Kieri, S. Holmgren, and H. O. Karlsson. An adaptive pseudospectral method for wave packet dynamics. J. Chem. Phys., 137:044111, 2012.
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[35] A. Uschmajew. Local convergence of the alternating least squares algorithm for canonical tensor approximation. SIAM J. Matrix Anal. Appl., 33(2):639-652, 2012.
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[36] S. Hosseini and M. R. Pouryayevali. Generalized gradients and characterization of epi-Lipschitz sets in Riemannian manifolds. Nonlinear Anal., 74(12):3884-3895, 2011.
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[37] A. Uschmajew. Regularity of tensor product approximations to square integrable functions. Constr. Approx., 34(3):371-391, 2011.
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[38] A. Uschmajew. Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations. Numer. Math., 115(2):309-331, 2010.
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Proceeding Papers:

[1] E. Kieri, C. Lubich, and H. Walach. Time-stepping of low-rank approximations with small singular values. Oberwolfach Rep., 13, 2016. To appear.
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[2] E. Kieri, C. Lubich, and H. Walach. Discretised dynamical low-rank approximation in the presence of small singular values. Oberwolfach Rep., 12:1516-1517, 2015.
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[3] A. Uschmajew. Some results concerning rank-one truncated steepest descent directions in tensor spaces. In 2015 International Conference on Sampling Theory and Applications (SampTA), pages 415-419, 2015.
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[4] A. Uschmajew and B. Vandereycken. Greedy rank updates combined with Riemannian descent methods for low-rank optimization. In 2015 International Conference on Sampling Theory and Applications (SampTA), pages 420-424, 2015.
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[5] A. Uschmajew and B. Vandereycken. Line-search methods and rank increase on low-rank matrix varieties. In Proceedings of the 2014 International Symposium on Nonlinear Theory and its Applications (NOLTA2014), pages 52-55, 2014.
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[6] A. Uschmajew, D. Kressner, and M. Steinlechner. Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. Oberwolfach Rep., 10(4):3296-3298, 2013.
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[7] A. Uschmajew. The regularity of tensor product approximations in L² in dependence of the target function. Oberwolfach Rep., 8(2):1802-1804, 2011.
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Thesis:

[1] A. Uschmajew. Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen. PhD thesis, Technische Universität Berlin, Jan. 2013.
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