Question on the implementation about separableoptimization.jl HOT 1 CLOSED

Hi! Thanks for the question, and sorry for the delayed response.

You're exactly right: We follow something a little closer to OSQP in terms of problem formulation that what we have in our own paper. The motivation is subtle, and pretty minor. It's so that the resulting KKT matrix (in equation (13) in our paper, (24) in the OSQP paper) is quasi-definite. This guarantees that the LDL factorization exists, regardless of how we permute the rows and columns of the KKT matrix.

It's actually pretty similar to adding regularization to the bottom right of the KKT matrix, and doing iterative refinement. The clever trick here is that the iterative refinement is essentially embedded in the ADMM iterations, so there aren't two iteration loops (ADMM and iterative refinement).

I'd love to hear more about your application! Feel free to message me.

from separableoptimization.jl.