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 the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.


ESAIM Control, Optimization and Calculus of Variations, Vol. 10 (2004) 409-425