Hölder metric regularity of set-valued maps

Authors:
Hélène Frankowska;Marc Quincampoix
Affiliations:
CNRS & Universitéé Pierre et Marie Curie (Paris 6), Combinatoire et Optimisation, 4 place Jussieu, 75252, Paris cedex 05, France;UMR CNRS 6205, Université de Bretagne Occidentale, Laboratoire de Mathématiques, 6 avenue Victor Le Gorgeu, 29200, Brest, France
Venue:
Mathematical Programming: Series A and B
Year:
2012

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Abstract

This paper is devoted to metric regularity of set-valued maps from a complete metric space to a Banach space. In particular we extend a known characterization of the regularity modulus to maps defined on reflexive spaces. The higher order metric regularity, i.e. an extension of metric regularity to Hölder context, is also investigated using high order variations of set-valued maps and results of similar nature are obtained for conical metric regularity.