Geodesic
Hypomonotonicity of the Normal Cone and Proximal Smoothness
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1313-1339
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We study the properties of the normal cone to a proximally smooth set. We give a complete characterization of a proximally smooth set through the monotonicity properties of its normal cone in an arbitrary uniformly convex and uniformly smooth Banach space. We also give the exact bounds for the right-hand side in the monotonicity inequality for the normal cone in terms of the moduli of smoothness and convexity of a Banach space.
Classification : 52A05, 52A40
Mots-clés : Proximal smoothness, hypomonotonicity, variational inequality, Frechet normal cone 
@article{JCA_2017_24_4_JCA_2017_24_4_a13,
     author = {G. M. Ivanov},
     title = {Hypomonotonicity of the {Normal} {Cone} and {Proximal} {Smoothness}},
     journal = {Journal of convex analysis},
     pages = {1313--1339},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a13/}
}
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G. M. Ivanov. Hypomonotonicity of the Normal Cone and Proximal Smoothness. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1313-1339. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a13/