c笔记 ref.      distr_opt_stat_learning_admm.html

Basis pursuit is the equality-constrained  minimization problem

In ADMM form, basis pursuit can be written as

The ADMM algorithm is then

The x-update, which involves solving a linearly-constrained minimum Euclidean norm problem, can be written explicitly as
 

4.4.3 Soft Thresholding

where the soft thresholding operator S is defined as

the comments on efficient computation from §4.2 apply

We can interpret ADMM for basis pursuit as reducing the solution of a least  norm problem to solving a sequence of minimum Euclidean norm problem