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:

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:

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.

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.