Separation property of continuously differentiable functions

Sanjo Zlobec

Vol. 19 No. 1 (2014)

Regular Articles

Separation property of continuously differentiable functions

Published 2013-12-15

Sanjo Zlobec

Sanjo Zlobec
Department of Mathematics and Statistics, McGill University

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Abstract

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.

Keywords

function separation property, method of convexification, convexifier, concavifier, global properties of the gradient, zero-derivative point

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Author Biography

Sanjo Zlobec

Professor of Mathematics