Software for reweighted L1 minmization? I am trying to solve a sparsity-promoting optimization problem. It is well known that the L1 norm is a good surrogate to the L0 norm, and it is studied in (Candes et al, 2008: Enhancing sparsity by reweighted L1 minimization https://arxiv.org/abs/0711.1612) that a better approximation can be obtained by successively reweighting the L1 norm penalization term, where the result of a step gives the new weights for the next iteration.
So far I am implementing this directly in my code but I wonder if there is any software/optimization package that does this automatically.
I am not sure that it will answer the question exactly, but it appears that the glmnet package (R : glmnet, Python : glmnet) do something similar : enforcing sparsity trough iteration.
A small exemple of what you can get : coefficients as a function of the L1 norm. You can see the number of non-zero coefficients (degrees of freedom) evolving .