Nonlinear error bounds for lower semicontinuous functions on metric spaces

Abstract

As a development of the theory of linear error bounds for lower semicontinuous functions defined on complete metric spaces, introduced in Aze et al. (Nonlinear Anal 49, 643–670, 2002) and refined in Aze and Corvellec (ESAIM Control Optim Calc Var 10, 409–425, 2004), we propose a similar approach to nonlinear error bounds, based on the notion of strong slope, the variational principle, and the change-of-metric principle, the latter allowing to obtain sharp estimates for such error bounds through a reduction to the linear case.