Subgradient algorithm

[j.fal...@gmail.com]

Is there a subgradient algorithm for manopt? I am thinking of minimizing the L1-norm of a matrix. My first guess is smoothing the L1- norm, but maybe there are more sophisticated methods.

[BM]

Hello, 

There are a number of sophisticated methods for L1 minimization.

However, at the moment Manopt does not have a subgradient implementation. 

Regards,

BM

[j.fal...@gmail.com]

Which L1 - method would you recommend in connection with Manopt?

[Nicolas Boumal]

Hello,

Optimization algorithms for nonsmooth cost functions on manifolds is an ongoing research topic. And as Bamdev mentioned, there is nothing yet in Manopt to handle such problems (although Manopt was designed to be able to handle them when algorithms become available).

For now, typically we use smoothing (pseudo-Huber loss, for example), which has its pros and cons.

Sorry that we do not have a more complete answer at the time. If you find a good way to handle your cost function, we woud love to hear about it here, if you wish.

Cheers,

Nicolas

[Nicolas Boumal]

In the examples that ship with the manopt release, there is a minimax problem on the sphere that uses a Huber-loss smoothing:

http://www.manopt.org/reference/examples/packing_on_the_sphere.html

[seu...@gmail.com]

Hello Nicolas,

I am trying to use Manopt to solve some optimization problem on complex circle manifolds, it really helps me a lot and I found it a powerful tool!

Furthermore, I want to know some more details about the complex circle manifolds and I asked help from Bamdev, but he told me that you are more familiar with this kind of manifold. So could you please provide me some references about optimization problem on this manifold?

Thank you very much!
Xianghao

[Nicolas Boumal]

Hello Xianghao,

This last question seemed more related to your other topic, so I answered there:

https://groups.google.com/d/msg/manopttoolbox/_WnGZ2LU5io/NDlvgiC7A94J

Cheers,

Nicolas