Maximal Points of Convex Sets in Locally Convex Topological Vector Spaces: Generalization of the Arrow–Barankin–Blackwell Theorem

Autor:	L.W. Woo, Robert K. Goodrich
Rok vydání:	2003
Předmět:	Convex hull Control and Optimization Applied Mathematics Mathematical analysis Convex set Subderivative Management Science and Operations Research Krein–Milman theorem Choquet theory Combinatorics Strictly convex space Locally convex topological vector space Absolutely convex set Mathematics
Zdroj:	Journal of Optimization Theory and Applications. 116:647-658
ISSN:	1573-2878 0022-3239
Popis:	In 1953, Arrow, Barankin, and Blackwell proved that, if C is a nonempty compact convex set in Rn with its standard ordering, then the set of points in C maximizing strictly positive linear functionals is dense in the set of maximal points of C. In this paper, we present a generalization of this result. We show that that, if C is a compact convex set in a locally convex topological space X and if K is an ordering cone on X such that the quasi-interiors of K and the dual cone K* are nonempty, then the set of points in C maximizing strictly positive linear functionals is dense in the set of maximal points of C. For example, our work shows that, under the appropriate conditions, the density results hold in the spaces Rn, Lp(Ω, μ), 1≤p≤∞, lp, 1≤p≤∞, and C (Ω), Ω a compact Hausdorff space, when they are partially ordered with their natural ordering cones.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c4b28da0c643885ec691907652da994f https://doi.org/10.1023/a:1023021604751 Zobrazit plný text záznamu Full text from SpringerLink