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.
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@univ-brest.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 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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