Separation of finitely many convex sets and data pre-classification

Abstract

In this paper we consider a generalization of the separation technique proposed in Gaudioso et al. (Optimization 59:1199-1210, 2011) and Grzybowski et al. (Optim. Methods Softw. 20:219-229, 2005) for the separation of finitely many compact convex sets A i, i I by another compact convex set S in a locally convex vector space. We construct separating sets by means of a generalized Demyanov difference.