Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

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.