Extend `solver_L1RLS` to `solver_L1RLS_W`

[RoyiAvital]

Hello,

Currently solver_L1RLS solves:

$$ 0.5 ||A x - b||^{2} + \lambda || x ||_{1} $$

Could it be extended to:

$$ 0.5 ||A x - b||^{2} + \lambda || W x ||_{1} $$

As done with other solvers?

Thank You.

[stephenbeckr]

You could solve that weighted problem with TFOCS using the fancier options, but in terms of directly extending solver_L1RLS, that would require replacing prox_l1 with a weighted version, and in general the weighted prox for l_1 is not computable in closed form (with a few exceptions, e.g., if W is diagonal or partial orthogonal... these are not directly implemented but you could make your own implementation or just make an explicit change-of-variables.