The Radius of Metric Regularity Revisited
Helmut Gfrerer, Alexander Y. Kruger · Set-Valued and Variational Analysis · 2023
Abstract The paper extends the radius of metric regularity theorem by Dontchev, Lewis and Rockafellar (2003) 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 a natural upper bound for the radius complementing the conventional lower bound in the theorem by Dontchev, Lewis and Rockafellar.