Separation of Finitely Many Convex Sets and Data Pre-classification

Manlio Gaudioso (), Jerzy Grzybowski (), Diethard Pallaschke () and Ryszard Urbański ()
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Manlio Gaudioso: Universita della Calabria, Dipartimento di Elettronica, Informatica e Sistemistica (DEIS)
Jerzy Grzybowski: Adam Mickiewicz University, Faculty of Mathematics and Computer Science
Diethard Pallaschke: University of Karlsruhe (KIT), Institute of Operations
Ryszard Urbański: Adam Mickiewicz University, Faculty of Mathematics and Computer Science

A chapter in Optimization in Science and Engineering, 2014, pp 179-188 from Springer

Abstract: 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.

Keywords: Compact Convex; Nonempty Closed Convex Subset; Compact Convex Subset; Finite Dimensional Space; Hausdorff Topological Vector Space (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0808-0_9

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