  This work aims at solving the problems with intractable sparsity-inducing
norms that are often encountered in various machine learning tasks, such as
multi-task learning, subspace clustering, feature selection, robust principal
component analysis, and so on. Specifically, an Iteratively Re-Weighted method
(IRW) with solid convergence guarantee is provided. We investigate its
convergence speed via numerous experiments on real data. Furthermore, in order
to validate the practicality of IRW, we use it to solve a concrete robust
feature selection model with complicated objective function. The experimental
results show that the model coupled with proposed optimization method
outperforms alternative methods significantly.
