Friday, 14:15 - 14:40 h, Room: H 2036


André Uschmajew
Convergence of algorithms on quotient manifolds of Lie groups


When it comes to analyzing the (local) convergence properties of algorithms for optimization with respect to certain tensor formats of fixed low rank, such as PARAFAC-ALS or TUCKER-ALS, one is confronted with the non-uniqueness of the low-rank representations, which causes naive contraction arguments to fail. This non-uniqueness is (at least partially) caused by a Lie group action on the parameters of the tensor format (scaling indeterminacy). On the other hand, for instance in the case of ALS, the algorithm has an invariance property (with respect to the Lie group), namely to map equivalent representations to equivalent ones.
In this talk we show how these ingredients lead to natural convergence results for the equivalence classes (orbits) of the Lie group, which are the true objects of interest. For subspace tensor formats, such as the Tucker format, the quotient manifold is diffeomorphic to the variety of tensors of fixed subspace rank. For the CP format one has to make additional assumptions. The results are presented in a generality which does not restrict them to the low-rank tensor approximation problem only


Talk 3 of the invited session Fri.2.H 2036
"Algebraic geometry and conic programming, part II" [...]
Cluster 4
"Conic programming" [...]


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