Optimization with product manifold

[rob...@umich.edu]

I am trying to use Manopt to solve optimization problems on product manifolds, which seem to be giving me problems since each element of a product manifold is a struct, not a matrix. Is there a way to work around this problem that anyone has found? in particular, I am having trouble with any time a solver needs to perform matrix multiplication.

[BM]

Hello Rob, 

I am a bit confused in trying to understand the problem that you are having. 

For example, if S is a structure with two fields, X and Y, then S.X and S.Y will be matrices and with these matrix multiplications can be handled...

Have I understood your question correctly?

Regards,

BM

[BM]

Hello, 

From the discussion earlier, it seems that there was an issue with the  pso.m solver of Manopt (for particle swarm optimization) while handling product manifold structures. It has now been corrected. The updated file is attached here.

A couple of things to note here.

1) This is not an official release of the pso.m file. In due time it will be.

2) PSO relies on definition of the log map on the manifold. This may not be defined on some manifolds provided. A workaround based on finite definite approximation is given but this also may not be sufficient in few cases. 

Regards,

Bamdev