Separation of convex sets by Clarke subdifferential

GAUDIOSO, MANLIO;GORGONE, ENRICO;Pallaschke, D.

2010-01-01

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Abstract

In this article we consider a separation technique proposed in J. Grzybowski, D. Pallaschke, and R. Urbanski (A pre-classification and the separation law for closed bounded convex sets, Optim. Method Softw. 20(2005), pp. 219-229) for separating two convex sets A and B with another convex set C. We prove that in a finite dimension C can be chosen as the Clarke subdifferential at the origin of minfpA,pBg, where pA, pB denotes the support functions of A and B respectively. © 2010 Taylor & Francis.