Felix Neussel – Optimization Online

On Supportedness-Promoting Image Space Transformations in Multiobjective Optimization

Published: 2025/11/26

Multi-Criteria Optimization lagrange duality, multiobjective optimization, power transformation, supportedness, Weighted sum scalarization

We study the supportedness of nondominated points of multiobjective optimization problems, that is, whether they can be obtained via weighted sum scalarization. One key question is how supported points behave under an efficiency-preserving transformation of the original problem. Under a differentiability assumption, we characterize the transformations that preserve both efficiency and supportedness as the component-wise … Read more

On image space transformations in multiobjective optimization

Published: 2025/04/30, Updated: 2025/11/25

Oliver Stein

Felix Neussel

Multi-Criteria Optimization compromise approach, monotonicity, multicriteria optimization, trade-off bound, transformation

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 be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points … Read more