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ALOP Colloquium with Dr. Bart Vandereycken
6. February 2017 / 16:00 - 18:00
Manifold optimization for low rank matrix and tensor completion
The minimisation of a smooth objective function subject to (matrix) rank constraints can sometimes be very effectively solved by methods from Riemannian optimisation. This is for instance the case with the low-rank matrix and tensor completion problems However, the standard theory of Riemannian optimisation leaves some questions unanswered regarding its theoretical and practical application. I will focus on two such questions. The first is how the (Riemannian) metric has a significant impact on the convergence of the numerical methods which I will illustrate by deriving recovery guarantees assuming RIP. The second topic is rank adaptivity. In rank-constrained optimisation, the rank is typically not known and instead one is searching for the smallest rank satisfying a certain criterion, like a small residual. I will explain how the geometry of the tangent cone of the variety of matrices of bounded rank can be incorporated so as to obtain rank adaptive algorithms that stay true to the manifold paradigm.
At 15:45 there will be a coffee hour in E10. The presentation will take place in HS9 at 16:15.