The Radius of Metric Regularity Revisited

TL;DR

This paper advances the understanding of metric regularity by providing an exact formula for the radius under Lipschitz perturbations in Asplund spaces, and offers bounds in non-Asplund spaces, answering a long-standing open question.

Contribution

It extends the 2003 theorem by deriving an exact radius formula in Asplund spaces and establishing bounds in non-Asplund spaces, resolving a 20-year-old open problem.

Findings

Exact radius formula for Lipschitz perturbations in Asplund spaces

Upper bounds for the radius in non-Asplund spaces

Resolution of an open question from 2003

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.