The Radius of Metric Regularity Revisited

Abstract

The paper extends the 2003 radius of metric regularity theorem by Dontchev, Lewis & Rockafellar by providing an exact formula for the radius with respect to Lipschitz continuous perturbations in general Asplund spaces, thus, answering affirmatively an open question raised twenty years ago by Ioffe. In the non-Asplund case, we give natural upper bounds for the radius complementing the conventional lower bound in the theorem by Dontchev, Lewis & Rockafellar.