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
Publication date:
26.5.2014.
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