Manopt and the optimisation on definite matrices

[Florian Yger]

Dear Nicolas and Bamdev,

First of all, thank you for this very useful toolbox.

I am currently looking at an optimisation problem under a strict definite positiveness contraint (ie $X \in R^{n \times n}$, $X=X^{T}$ and $X>0$, so rank(X)=n). I think it would be interesting to use the inherent Riemannian geometry of the problem (with the affinte invariant metric).

As symmetric positive definite matrices are not in the manifolds factory of manopt, I was wondering if I would be wise to use fixed-rank symmetric matrices (with k=n) in order to tackle this problem. Could you give me your opinion on this ?

Thanks in advance

[BM]

Hello Florian, 

Here are the test and geometry files for the set of positive definite cone with the bi-invariant geometry. In the next release we will include these files officially. Do share with us your experience and do not hesitate to ask any other question that you may have.

Regards,

Bamdev

[Florian Yger]

Thank you very much for your answer and your reactivity.

Best regards.
Florian

[Nicolas Boumal]

These geometry files have since then been updated and will appear in the next release of Manopt (1.0.6). You can already access them on the forum, in a thread started on January 19, 2014 if need be.

- Nicolas