The investigation of nonlinear scalarizing functions for sets began around twenty years ago. Recently, many authors have investigated nonlinear scalarization techniques for set optimization problems. In this presentation, first we look back into the history of nonlinear scalarization techniques for sets, and introduce three important papers published in the 2000s. Afterwards, we present recent advances on this topic.
joint work with Bahareh Khazayel, Christiane Tammer, Ali Farajzadeh
Penalization approaches in multi-objective optimization aim to replace the original constrained optimization problem by some related problems with an easier structured feasible set (e.g., unconstrained problems). One approach, namely the Clarke-Ye type penalization method, consists of adding a penalization term with respect to the feasible set in each component function of the objective function. In contrast, the vectorial penalization approach is based on the idea to add a new penalization (component) function to the vector-valued objective function. In this talk, we compare both approaches.
This talk discusses the application of the reference point method to convex multiobjective optimization problems with arbitrarily many cost functions. The main challenge of the reference point method in the case of more than two cost functions is to find reference points which guarantee a uniform approximation of the whole Pareto front. In this talk we develop a theoretical description of the set of 'suitable' reference points, and show how this can be used to construct an iterative numerical algorithm for solving the multiobjective optimization problem.