Characterize robust noncriticality and its convergence implications

Characterize the interrelations among the stronger noncriticality notions obtained by replacing the ordinary graphical derivative with robust derivative constructions, and determine whether these notions can yield superlinear convergence of Newton-type methods.

Background

The conclusions identify a broader research program based on replacing the ordinary graphical derivative in the definition of noncriticality with robust counterparts. The paper leaves unresolved both the relationships among the resulting family of stronger notions and their ability to support superlinear convergence guarantees for Newton-type methods. The semi-strict graphical derivative is singled out as a particularly promising candidate.

References

As discussed in \cref{sec:perturbations}, replacing the graphical derivative by one of its robust counterparts gives rise to a whole family of stronger notions, and their interrelations, as well as their potential to yield superlinear convergence of Newton-type methods, remain to be explored.

— On error bounds and noncritical Lagrange multipliers  (2610.11491 - Benko et al., 8 Oct 2026) in Section 7, “Conclusions”