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Wissenschaftliche Mitarbeiter

Dr. Paul Breiding


Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Raum MA 303 (3. OG)
Institut für Mathematik

Persönliche Homepage:


Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771


+49 (0)30 314 - 73990
+49 (0)30 314 - 25839

Während der Vorlesungszeit: Nach Vereinbarung.
Während der vorlesungsfreien Zeit: Nach Vereinbarung.

Publikationen in der Arbeitsgruppe

A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem
Citation key BV-A-Riemannian-Trust-Region-Method-For-The-Canonical-Tensor-Rank-Approximation-Problem
Author Paul Breiding and Nick Vannieuwenhoven
Year 2017
Month 09
Abstract The canonical tensor rank approximation problem (TAP) consists of approximating a real-valued tensor by one of low canonical rank, which is a challenging non-linear, non-convex, constrained optimization problem, where the constraint set forms a non-smooth semi-algebraic set. We introduce a Riemannian Gauss-Newton method with trust region for solving small-scale, dense TAPs. The novelty of our approach is threefold. First, we parametrize the constraint set as the Cartesian product of Segre manifolds, hereby formulating the TAP as a Riemannian optimization problem, and we argue why this parametrization is among the theoretically best possible. Second, an original ST-HOSVD-based retraction operator is proposed. Third, we introduce a hot restart mechanism that efficiently detects when the optimization process is tending to an ill-conditioned tensor rank decomposition and which often yields a quick escape path from such spurious decompositions. Numerical experiments show improvements of up to three orders of magnitude in terms of the expected time to compute a successful solution over existing state-of-the-art methods.
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