Characterizations of error bounds for lower semicontinuous functions on metric spaces
UMR CNRS MIP, Université Paul Sabatier,
118 route de Narbonne, 31062 Toulouse Cedex, France; firstname.lastname@example.org.
2 Laboratoire MANO, Université de Perpignan, 52 avenue de Villeneuve, 66860 Perpignan Cedex, France.
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.
Mathematics Subject Classification: 49J52 / 90C26 / 90C25 / 49J53
Key words: Error bounds / strong slope / variational principle / metric regularity.
© EDP Sciences, SMAI, 2004