Separation property of continuously differentiable functions

Sanjo Zlobec


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.


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

Full Text:


ISSN: 1331-0623 (Print), 1848-8013 (Online)