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Nonlinear local error bounds via a change of metric

Dominique Azé (dominique.aze***at***math.univ-toulouse.fr)
Jean-Noël Corvellec (corvellec***at***univ-perp.fr)

Abstract: In this work, we improve the approach of Corvellec-Motreanu to nonlinear error bounds for lowersemicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and allows dealing with local error bounds in an appropriate way. We present some consequences of the general results in the framework of classical nonsmooth analysis, involving Banach spaces and subdifferential operators. In particu- lar, we describe connections between local quadratic growth of a function, and metric regularity of its subdifferential.

Keywords: Non linear metric regularity, nonlinear error bounds, slope.

Category 1: Convex and Nonsmooth Optimization

Category 2: Infinite Dimensional Optimization

Category 3: Nonlinear Optimization

Citation: Institut de Mathématiques de Toulouse and université de Perpignan, September 2014


Entry Submitted: 10/23/2014
Entry Accepted: 10/23/2014
Entry Last Modified: 02/05/2019

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