Hoffman's error bound, local controllability, and sensitivity analysis

Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its im pact on the local controllability, implicit function theorem for (non-Lipsc hitz) multivalued mappings, generalized equations (variational inequalities ), and sensitivity analysis and on other problems like Lipschitzian propert ies of polyhedral multivalued mappings as well as weak sharp minima or line ar conditioning. We show how the information about our sufficient condition s can be used to provide a computable constant such that Hoffman's error bo und holds. We also show that this error bound is nothing but the classical Farkas lemma for linear inequality systems. In the latter case our constant may be computed explicitly.