Some Fundamental Theorems

Johannes Jahn ()
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Johannes Jahn: Universität Erlangen-Nürnberg

Chapter Chapter 3 in Vector Optimization, 2011, pp 61-100 from Springer

Abstract: Abstract For the investigation of vector optimization problems we need various fundamental theorems of convex analysis which are presented in this section. First, we formulate Zorns lemma and the Hahn-Banach theorem and, as a consequence, we examine several types of separation theorems. Moreover, we discuss a James theorem on the characterization of weakly compact sets and we study two Krein-Rutman theorems on the extension of positive linear functionals and the existence of strictly positive linear functionals. Finally, we prove a Ljusternik theorem on certain tangent cones.

Keywords: Convex Cone; Nonempty Subset; Fundamental Theorem; Basic Version; Separation Theorem (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-17005-8_3

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DOI: 10.1007/978-3-642-17005-8_3

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