About isermann duality

In this note, we consider the following multiple-objective linear program: maxCx, such thatAx=b,x≧0, and its associated Isermann dual program: minUb, such thatUAW≤Cw, for now≧0. We give a simple proof of the known fact that, for every dual efficient pointU°, there is a primal efficient pointx°, such thatU°b=Cx°. Parts of the ingredients in this proof are useful in exploring the structure of the dual feasible set of function values {Ub¦UAw≤Cw, for now≧0}.