Geometric duality and parametric duality for multiple objective linear programs are equivalent

In 2011, Luc introduced parametric duality for multiple objective linear programs. He showed that geometric duality, introduced in 2008 by Heyde and L\"ohne, is a consequence of parametric duality. We show the converse statement: parametric duality can be derived from geometric duality. We point out that an easy geometric transformation embodies the relationship between both duality theories. The advantages of each theory are discussed.