We show that every continuously differentiable function in several variables with a global Lipschitz derivative on a compact convex set has a separation property. It separates two classes of quadratic functions given in terms of either the function’s convexifiers or its concavifiers. The separation is used to obtain new global properties of the derivative and characterizations of zero derivative points.
Publié le : 2014-06-10
Classification:
function separation property; method of convexification; convexifier; concavifier; global properties of the gradient; zero-derivative point,
26A06; 26A24; 26A36; 26B20; 90C30
@article{mc393,
author = {Zlobec, Sanjo},
title = {Separation property of continuously differentiable functions},
journal = {Mathematical Communications},
volume = {19},
number = {1},
year = {2014},
pages = { 57-64},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc393}
}
Zlobec, Sanjo. Separation property of continuously differentiable functions. Mathematical Communications, Tome 19 (2014) no. 1, pp. 57-64. http://gdmltest.u-ga.fr/item/mc393/