Actually approachable math - senior undergrad math major or first year grad can easily understand what's going on. ADMM is actually very old primal dual setup solved via Lagrangian, goes back to 1980s I think. Good reference - https://web.stanford.edu/~boyd/papers/pdf/admm_slides.pdf

The article itself refers to Boyd's Convex Optimization textbook, which is sort of a rite of passage for anybody doing anything math-related at Stanford these days - even their MS in Management course requires a semester of convex optimization.