ADMM

we propose an Alternating Direction Method of Multipliers (ADMM) scheme for a broad class of convex slack penalty functions, including all ℓk-norms, without increasing the problem size. The only change to the ADMM scheme is a modified slack projection function, while the remaining algorithm stays the same. We demonstrate our approach on numerical examples, showing significant speedups, and show its flexibility on an energy optimization problem.

We propose a simple ADMM scheme to tackle QPs with slack variables without increasing the size of the original problem. The only modification is a slightly different projection in the z-update, while the rest of the algorithm remains standard. We prove that the method is equivalent to applying ADMM to the QP with additional slack variables, even though slack variables are not added. Numerical experiments show speedups of the approach.