Original scientific paper

Separation property of continuously differentiable functions

Sanjo Zlobec ; Department of Mathematics and Statistics, McGill University, Burnside Hall, Montreal, Quebec, Canada

Abstract

We show that every continuously differentiable function in several variables with a global Lipschitz derivative on a compact convex set with interior points 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 characterizations of the derivative and zero derivative points.

Keywords

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

Hrčak ID:

121825

URI

https://hrcak.srce.hr/121825

Publication date:

26.5.2014.

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