2011 | OriginalPaper | Chapter
Some Fundamental Theorems
Author : Prof. Dr. Johannes Jahn
Published in: Vector Optimization
Publisher: Springer Berlin Heidelberg
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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.