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Journal of Convex Analysis 13 (2006), No. 2, 281--297
Copyright Heldermann Verlag 2006

Aubin Criterion for Metric Regularity

A. L. Dontchev
Mathematical Reviews, Ann Arbor, MI 48107, U.S.A.

M. Quincampoix
Lab. de Mathématiques, UMR CNRS 6205, Université de Bretagne Occ., 6 Av. Victor Le Gorgeu, 29200 Brest, France

N. Zlateva
Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria

We present a derivative criterion for metric regularity of set-valued mappings that is based on works of J.-P. Aubin and co-authors. A related implicit mapping theorem is also obtained. As applications, we first show that Aubin criterion leads directly to the known fact that the mapping describing an equality/inequality system is metrically regular if and only if the Mangasarian-Fromovitz condition holds. We also derive a new necessary and sufficient condition for strong regularity of variational inequalities over polyhedral sets. A new proof of the radius theorem for metric regularity based on Aubin criterion is given as well.

Keywords: Set-valued mappings, metric regularity, variational analysis, graphical derivative, implicit mapping theorem, variational inequality, strong regularity.

MSC: 49J53, 90C31

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