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.
Mots clés : error bounds, strong slope, variational principle, metric regularity
@article{COCV_2004__10_3_409_0, 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://www.numdam.org/articles/10.1051/cocv:2004013/} }
TY - JOUR AU - Azé, Dominique AU - Corvellec, Jean-Noël TI - Characterizations of error bounds for lower semicontinuous functions on metric spaces JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 409 EP - 425 VL - 10 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004013/ DO - 10.1051/cocv:2004013 LA - en ID - COCV_2004__10_3_409_0 ER -
%0 Journal Article %A Azé, Dominique %A Corvellec, Jean-Noël %T Characterizations of error bounds for lower semicontinuous functions on metric spaces %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 409-425 %V 10 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2004013/ %R 10.1051/cocv:2004013 %G en %F COCV_2004__10_3_409_0
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. http://www.numdam.org/articles/10.1051/cocv:2004013/
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