ESAIM: Control, Optimisation and Calculus of Variations

Research Article

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Azé, Dominiquea1 and Corvellec, Jean-Noëla2

a1 UMR CNRS MIP, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France; aze@mip.ups-tlse.fr.

a2 Laboratoire MANO, Université de Perpignan, 52 avenue de Villeneuve, 66860 Perpignan Cedex, France.

Abstract

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.

(Received May 8 2003)

(Online publication June 15 2004)

Key Words:

  • Error bounds;
  • strong slope;
  • variational principle;
  • metric regularity.

Mathematics Subject Classification:

  • 49J52;
  • 90C26;
  • 90C25;
  • 49J53
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