Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization

In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed.