Methods for multiobjective bilevel optimization

This paper is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems by means of scalarization functionals and optimality conditions. These can be used in theoretical and numerical approaches to multiobjective bilevel optimization. As multiple objectives arise in multiobjective optimization as well as in bilevel optimization problems, we also point out the results on the connection between these two classes of optimization problems. Finally, we given reference to numerical approaches which have been followed in the literature to solve these kind of problems. We concentrate in this paper on nonlinear problems, while the results and statements then naturally also hold for the linear case.



View Methods for multiobjective bilevel optimization