Value functions, domination cones and proper efficiency in multicriteria optimization

In the absence of a clear ‘objective’ value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. The paper shows that such cones must be convex, strictly supported and, frequently closed as well. Furthermore, in most applications ‘potential’ optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.