Efficiency-Preserving Transformations in Multiobjective Optimization: Characterizations and Effect on Trade-Off Bounds

This paper considers monotone transformations of the objective space of multiobjective optimization problems which leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone we show that such transformations must necessarily be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points invariant. In addition, our approach allows to specify trade-off bounds of properly efficient points after the transformation. We apply our results to prove some previously unknown properties of the compromise programming approach.