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.