ADMM formalization I found lots of examples of ADMM formalization of equality constraint problems (all with single constraint). I am wondering how to generalize it for multiple constraints with mix of equality and inequality constraints.
I have a problem

Minimize $||A_x||_1 + \lambda ||A_y||_2 $, such that:
  $$A_x X = A_x$$
      $$\mathrm{diag}(A_x) = 0$$
      $$A_x \ge 0$$
      $$A_y \le 0$$

How can I write this in ADMM form ?.

The "constraint" $Ax+Bz=c$ is there to introduce variable splitting. The actual (problem) constraints are introduced through indicator functions (e.g. $g(z) = \mathbf{1}_{\|\cdot\| \leq \varepsilon} (z)$). To allow for multiple constraints, you can reformulate your problem such that $f$ or $g$ represents a sum of penalty functions (approach known as SDMM, check this paper).
