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 $\ell_1$ sparse group lasso problem and the $\ell_0$ sparse group lasso problem. Also, we propose the algorithms for computing these bounds.

翻译：我们提出了一种用于通用重叠组Lasso问题的乘子交替方向法（ADMM），其中组可以以任意方式重叠。同时，我们证明了$\ell_1$稀疏组Lasso问题和$\ell_0$稀疏组Lasso问题的下界与上界。此外，我们还提出了计算这些边界的算法。