A hahn-banach theorem in ordered linear spaces and its applications

Abstract

In this paper, a weak version of Hahn-Banach theorem is derived for convex relations in ordered linear spaces in which a separation theorem of convex sets in [11] is used. Then this result is applied to derive existence of weak Lagrange multiplier theorem for the following vector optimization problem:

where F,H are convex relations from a linear space X to an ordered linear space Y.We also prove existence of weak subgradient for convex relations by using Hahn-Banach theorem. A partial extension of the subgradient formula in [2] to ordered space is obtained

Keywords:

• Ordered linear Space
• Convex Relation
• Hahn-Banach Theorem
• Weak Lagrange Multiplier
• Weak subgradient