L1-norm with CVX and ill-conditioned matrix

1

Hi everyone.

I have been using CVX to solve this problem (1):

l1-reg.jpg795×133 13.8 KB

If the A matrix is ill-conditioned, what are the effects on the SDTP3 algorithm performance? I have a limited set of matrices and I may choose one to use in (1). I probed a matrix best conditioned and the results were better than in other cases.

What is the theory that I can use to justify the need of the a matrix better conditioned in CVX?

Thank you very much!

2

There are so many good algorithms out there to solve this problem.
Why would you do it using CVX?

3

Hi, I tested several algorithm as YALL1, GPSR and L1_Ls. The GPSR and L1_ls results are the same compared to CVX. Also CVX is most fast in my database de 2400 optimization cases. I know that (1) is a convex problem and CVX exploits this problem structure.

4

I agree with you Royi, CVX is not the right tool for this job.

5

I don’t know the packages you used to solve it.

But CVX main power is solving any Convex Problem given it can formulated under the DCP rules.
It pays for this amazing flexibility with efficiency, namely, if you know how to solve your problem probably you’d do it better than CVX.

{L}_{1} regularized Least Squares is something so popular you really should solve it differently.