The natural ordering cone of a polyhedral convex set-valued objective mapping

Abstract

For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behavior of a polyhedral convex set optimization problem can be characterized by this cone. Under appropriate assumptions the natural ordering cone is proven to be the smallest ordering cone which makes a polyhedral convex set optimization problem solvable.

arXiv commentnew in this version: Corollary 3.5 added, some minor changes