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<p>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&#xa0;-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&#xa0;-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.</p>

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Multi-Objective Optimization and its Connection to Multivariate Risk Measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月3日

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  • Elisa Mastrogiacomo,
  • Matteo Rocca,
  • Marco Tarsia

摘要

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.