Multi-Objective Optimization and its Connection to Multivariate Risk Measures

Abstract In this paper, we generalize the study of minimax stochastic programming to the case where the objective function is multi-objective. We adopt a component -wise worst-case approach and provide necessary and sufficient conditions for optimality in terms of suitable first-order conditions. We then compare the proposed method with the minimization of vector -valued risk measures, as developed progressively in the literature over the past decades. We show that minimizing a certain class of multivariate risk measures is, in a precise sense, equivalent to solving a multi-objective expected value optimization problem with respect to some appropriate admissible distributions. We also analyze specific optimization problems involving risk functionals.