Characterizations of error bounds for lower semicontinuous functions on metric spaces

Azé, Dominique; Corvellec, Jean-Noël

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 409-425.

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], 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 (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.

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