Steepest descent of Grassmannian Manifold

[Muntadher Q Alsabah]

Hi all,

First of all, I would like to thank you very much for the cooperation in providing an instruction on how to use the optimization over the manifold. 

I am really interested in solving my optimization problem with the Grassmannian manifold. 

I have tried to implement an optimization algorithm (minimization the MSE) under Unitary constraint with the help of Grassmannian Manifold. 

I really need your help since I have problem with the algorithm convergence to the optimum matrix that minmizes the MSE cost function. 

I have attached to you the code and the function and looking forward for your kind help. If you need any further information please let me know.

Many thanks in advance,

Muntadher 

[Nicolas Boumal]

Hello Muntadher,

I had a look at your files, but don't see where the cost function is. Stiefel and Grassmann (in the standard files of Manopt) deal with matrices of size n x p with orthonormal columns as input. I didn't find a function with such input in your files.

You can also have a look at the examples folder of the toolbox, where some examples on the stiefelfactory or grassmannfactory are given. A good example for you perhaps is dominant_invariant_subspace, and there is also a complex version in the same folder.

Best,

Nicolas

[Muntadher Q Alsabah]

Dear Nicolas,

Thank you very much for the reply. I got it. 

Best regards,