
Journal of Convex Analysis 13 (2006), No. 2, 281297 Copyright Heldermann Verlag 2006 Aubin Criterion for Metric Regularity A. L. Dontchev Mathematical Reviews, Ann Arbor, MI 48107, U.S.A. ald@ams.org M. Quincampoix Lab. de Mathématiques, UMR CNRS 6205, Université de Bretagne Occ., 6 Av. Victor Le Gorgeu, 29200 Brest, France Marc.Quincampoix@univbrest.fr N. Zlateva Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria zlateva@math.bas.bg We present a derivative criterion for metric regularity of setvalued mappings that is based on works of J.P. Aubin and coauthors. 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 MangasarianFromovitz 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: Setvalued mappings, metric regularity, variational analysis, graphical derivative, implicit mapping theorem, variational inequality, strong regularity. MSC: 49J53, 90C31 [ Fulltextpdf (458 KB)] for subscribers only. 