Nonlinear local error bounds via a change of metric

In this work, we improve the approach of Corvellec-Motreanu to nonlinear error bounds for lowersemicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and allows dealing with local error bounds in an appropriate way. … Read more

Characterizations of error bounds for lower semicontinuous functions on metric spaces

By using a variational method based on Ekeland’s principle, we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces, and … Read more