Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications

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.