Journal of Convex Analysis 24 (2017), No. 4, 1313--1339
Copyright Heldermann Verlag 2017
Hypomonotonicity of the Normal Cone and Proximal Smoothness
Grigory M. Ivanov
Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny - Moscow region 141700, Russia
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.
Keywords: Proximal smoothness, hypomonotonicity, variational inequality, Frechet normal cone.
MSC: 52A05, 52A40.
[ Fulltext-pdf (305 KB)] for subscribers only.