This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approach, namely, by establishing the necessary optimality condition for a (local) optimal solution to a robust minimax optimization problem under a suitable constraint qualification, we then employ it to arrive in the desired target. In addition, some duality results for both robust minimax optimization problems and robust multi-objective optimization problems are also provided.

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极小极大编程作为研究鲁棒多目标优化问题的工具

本文旨在研究具有局部 Lipschitzian 数据的鲁棒多目标优化问题的弱帕累托解的最优条件。我们通过使用极大极小规划方法来做到这一点，即通过在合适的约束条件下为稳健极小极大优化问题的（局部）最优解建立必要的最优条件，然后我们使用它来达到所需的目标。此外，还提供了鲁棒极大极小优化问题和鲁棒多目标优化问题的一些对偶结果。