Projection of polyhedral cones and linear vector optimization

Consider a polyhedral convex cone which is given by a finite number of linear inequal-ities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We define a cone projection prob-lem using the data of a given linear vector optimization problem and consider the problem to determine the extreme directions and a basis of the lineality space of the projected cone K. The result of this problem yields a solution of the linear vector optimization problem. Analogously, the dual cone projection problem is related to the polar cone of K: One obtains a solution of the geometric dual linear vector optimization problem. We sketch the idea of a resulting algorithm for solving arbitrary linear vector optimization problems and provide an alternative proof of the geometric duality theorem based on duality of polytopes