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.

Separation of convex sets by Clarke subdifferential

GAUDIOSO, MANLIO;GORGONE, ENRICO;
2010

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.
Convex analysis; Data classification; Non-smooth optimization; Applied Mathematics; Control and Optimization; Management Science and Operations Research
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/212580
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