Preprint A24/2001
Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications

Mikhail Solodov | Izmailov, Alexey

**Keywords: **
error bounds; 2-regularity; complementarity

We obtain local estimates of the distance
to a set defined by equality constraints under assumptions which are
weaker than those previously used in the literature.
Specifically, we assume that the constraints mapping has a
Lipschitzian derivative, and satisfies a certain 2-regularity
condition at the point under
consideration. This setting directly subsumes the classical regular
case and the twice differentiable 2-regular case, for which
error bounds are known, but it is significantly richer than
either of these two cases.
When applied to a certain equation-based reformulation of the nonlinear
complementarity problem,
our results yield an error bound under an assumption
more general than $b$-regularity. The latter appears to be the weakest
assumption
under which a local error bound for complementarity problems was
previously available.
We also discuss an application of our results to the
convergence rate analysis of the exterior penalty method for
solving irregular problems.