An ADMM Algorithm for a Generic ${\mathrm{\ell }}_0$ Sparse Overlapping Group Lasso Problem

We present an alternating direction method of multipliers (ADMM) for a generic overlapping group lasso problem, where the groups can be overlapping in an arbitrary way. Meanwhile, we prove the lower bounds and upper bounds for both the ${\mathrm{\ell }}_1$ sparse group lasso problem and the ${\mathrm{\ell }}_0$ sparse group lasso problem. Also, we propose the algorithms for computing these bounds.