About Hahn-Banach extension theorems and applications to set-valued optimization

作者：Hernandez Elvira^*; Rodriguez Marin Luis; Sama Miguel

来源：Computers & Mathematics with Applications, 2012, 64(6): 1778-1788.

DOI：10.1016/j.camwa.2012.02.013

• Hahn-Banach theorem
• Set-valued map
• Affine selection
• Set optimization
• Lagrange multiplier theorem
• Affinelike map

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.

• 出版日期2012-9