Geodesic
Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential
Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1165-1192.

Voir la notice de l'article provenant de la source Heldermann Verlag

This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefiniteness properties of the second-order subdifferential (or generalized Hessian).
Classification : 49J52, 49J53, 90C31
Mots-clés : Variational analysis, quadratic growth, first-order and second-order generalized differentiation, metric regularity and subregularity, prox-regular functions, tilt stability in optimization 
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     author = {D. Drusvyatskiy and B. S. Mordukhovich and T. T. A. Nghia},
     title = {Second-Order {Growth,} {Tilt} {Stability,} and {Metric} {Regularity} of the {Subdifferential}},
     journal = {Journal of convex analysis},
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     volume = {21},
     number = {4},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a12/}
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D. Drusvyatskiy; B. S. Mordukhovich; T. T. A. Nghia. Second-Order Growth, Tilt Stability, and Metric Regularity of the Subdifferential. Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1165-1192. http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a12/