I have a problem with a quadratic objective function and non linear constraints. I can solve this problem in general by using a non linear optimizer, but it takes too long to be useful. I can solve this problem (most of the time) using OSQP by creating locally linearized constraints. The 1st derivative of the constraints is discontinuous at 0 so I have to split it into a set where the domain is positive and another where the domain is negative. I then iterate by solving it with some initial constraints, use the Lagrange multipliers (I’m assuming that’s what results.y is) to determine which positive domain constraints want to become negative domain constraints (and vice versa) and switch some of them.

As I said, this works most of the time, but in some cases, the initial constraints I have chosen are infeasible in some way, and in these cases, I can manually fiddle with them to get it started. So I want to automate this fiddling. Can the primal in-feasibility certificate be useful for this task?