Af. Izmailov et Mv. Solodov, Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications, MATH PROGR, 89(3), 2001, pp. 413-435
We obtain local estimates of the distance to a set defined by equality cons
traints under assumptions which are weaker than those previously used in th
e literature, Specifically, we assume that the constraints mapping has a Li
pschitzian derivative, and satisfies a certain 2-regularity condition at th
e point under consideration. This setting directly subsumes the classical r
egular case and the twice differentiable 2-regular case, for which error bo
unds are known, but it is significantly richer than either of these two cas
es. When applied to a certain equation-based reformulation of the nonlinear
complementarity problem, our results yield an error bound under an assumpt
ion more general than b-regularity. The latter appears to be the weakest as
sumption under which a local error bound for complementarity problems was p
reviously available. We also discuss an application of our results to the c
onvergence rate analysis of the exterior penalty method fur solving irregul
ar problems.