For many reasons, duality assertions are very important in optimization theory from the theoretical as well as from the numerical point of view. The duality theory of linear programming may serve as a model of what one can expect in the best case: A dual program can be stated explicitly and if it is solvable, so is the original problem, and vice versa. In this case, the optimal values coincide, ie no duality gap occurs. Establishing results of this type was an important task of linear programming theory right from the beginning; compare eg GL Dantzig’s book [5].

Duality for multicriteria optimization problems is more complicated than for single objective optimization problems. Usually, duality theorems are proved by scalarizing the cost function. Proceeding in this way, it is possible to apply duality assertions for scalar optimization problems and finally, the conclusions have to be translated back into the context of the vector-valued case. The last step often requires some additional assumptions.