Modification to Basis Pursuit Denoising Problem

TFOCS
1

Hello All! I am new to this community and would really appreciate if someone can help me with my query. I need to solve a basis pursuit problem of the following form where m should be between -1 to 1:
bpdn
I have two questions:

First, can this problem be solved by function ‘solver_sBPDN_W’? If yes, how? Because this problem is unconstrained formulation and in case of the mentioned function, I need to give inputs for epsilon and mu which is in form of:

minimize norm(Wx,1) + 0.5mu(x-x0).^2
s.t. norm(A*x-b,2) <= epsilon

Second, the L2 norm term in my problem is not squared and multiplied by 0.5 like the standard unconstrained formulation as below:

                               min(0.5*(||Ax-b||_2)^2+lambda*||x||_1)

In summary, how do I solve my modified problem and ensuring -1 =< m =< 1?

Thank you!

2

Unfortunately, there may not be any TFOCS developers or advanced users who are still active on this forum. So don’t be surprised if you don;t get any TFOCS help. You can of course look at old TFOCS posts on this forum and see if that helps; for instance, Using TFOCS for Scaled Basis Pursuit Denoising and many others.

If you wish to solve this using CVX, it is straightforward to enter.

1 Like
3

Thank you Mark for your reply. I understand what you are saying. Actually, CVX is working fine but it is slow. I felt that TFOCS will be much faster.

4

Which optimizer are you using with CVX?

5

I am using the default one. Disciplined convex programming.

6

CVX cannot optimize anything but must call an optimizer. Typically CVX calls for instance SeDuMi, SDTP3, or Mosek to do the optimization. There can be a huge difference in solution time depending which optimizer you use.

If the fastest optimizer which is likely to be Mosek is not fast enough then post the log output in a reply.

In any case I would recommend you spend some time understanding how Cvx actually works before moving to TFOCS. You are likely to do yourself a big favor then.