  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.
