About Hahn-Banach extension theorems and applications to set-valued optimization
In this paper we revise several generalizations of the algebraic Hanh-Banach extension theorem for set-valued maps and give new versions in terms of set-relations and selections. We apply our results by establishing optimality conditions for a set-valued constrained optimization problem considering several types of solutions. Finally, we give necessary conditions for the existence of affine selections via affinelike maps in the framework of linear spaces. (c) 2012 Elsevier Ltd. All rights reserved.
set-valued map affine selection affinelike map hahn-banach theorem set optimization lagrange multiplier theorem