This article is cited in 1 paper

On the representability of a function of two variables as the difference of two convex functions

I. M. Prudnikov

Smolensk Division of the Russian University of Cooperation, Smolensk, Russia

Abstract: We give necessary and sufficient conditions for the representability of an arbitrary function of two variables as the difference of two convex functions. Some geometric interpretation of these conditions is given. We present an algorithm of such a representation which yields a uniformly convergent sequence of convex functions.

Keywords: Lipschitz function, convex function, variation, curvature, rotation.

UDC: 517.172.4

Received: 17.06.2013
Revised: 10.05.2014

 English version: Siberian Mathematical Journal, 2014, 55:6, 1116–1125

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