Iterative refinement automatically accepts non-converged solutions

[Mersoltane]

When iterative refinement fails to converge, Amigo silently returns an inaccurate Newton direction. The line search then collapses the step size to zero, and from the outside there is no way to tell whether the failure is in the linear solve or in the line search.

[gjkennedy]

If iterative refinement fails and the linear solver does not produce a descent direction and the KKT conditions are not satisfied, then should we enter feasibility restoration? My question is, is this a specific bug with the solver or also an issue we should address in the IPM algorithm. It could be both!

[Mersoltane]

Yes, both. The iterative refinement retry path adds more delta_c regularization to recover a near-singular matrix at the solver level. When that hits the regularization cap and the linear solve still cannot produce a usable direction, the IPM should transition to feasibility restoration. I would keep this issue scoped to the solver-level retry, and once that is in we can handle routing the persistent linear-solve failures into the existing heuristic restoration.