Conic separation for vector optimization problems

Abstract

In this article, we analyse the relationships between conic and vector separation of two sets. Applying such results in the image space associated with a vector optimization problem (VOP), we show that the existence of a particular instance of vector separation is equivalent to the existence of a vector saddle point for the Lagrangian function associated with the VOP.

Keywords:

• vector optimization
• separation
• image space
• vector saddle point

AMS Subject Classifications::

• 90C
• 49J