Geodesic
Characterizations of error bounds for lower semicontinuous functions on metric spaces
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 409-425

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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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     author = {Az\'e, Dominique and Corvellec, Jean-No\"el},
     title = {Characterizations of error bounds for lower semicontinuous functions on metric spaces},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {409--425},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {3},
     year = {2004},
     doi = {10.1051/cocv:2004013},
     mrnumber = {2084330},
     zbl = {1085.49019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004013/}
}
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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, Tome 10 (2004) no. 3, pp. 409-425. doi: 10.1051/cocv:2004013

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