Characterizations of error bounds for lower semicontinuous functions on metric spaces
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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.

DOI: 10.1051/cocv:2004013
Classification: 49J52,  90C26,  90C25,  49J53
Keywords: error bounds, strong slope, variational principle, metric regularity
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     title = {Characterizations of error bounds for lower semicontinuous functions on metric spaces},
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Azé, Dominique; Corvellec, Jean-Noël. Characterizations of error bounds for lower semicontinuous functions on metric spaces. ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 3, pp. 409-425. doi : 10.1051/cocv:2004013. http://www.numdam.org/articles/10.1051/cocv:2004013/

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