In this paper, by means of linear and nonlinear (regular) weak separation functions, we obtain some characterizations of robust optimality conditions for uncertain optimization problems, especially saddle point sufficient optimality conditions. Additionally, the relationships between three approaches used for robustness analysis: image space analysis, vector optimization and set-valued optimization, are discussed. Finally, an application for finding a shortest path is given to verify the validity of the results derived in this paper.

中文翻译：

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通过图像空间分析对不确定优化问题的鲁棒性表征

在本文中，我们通过线性和非线性（正则）弱分离函数，获得了不确定优化问题的鲁棒最优条件的一些表征，特别是鞍点充分最优条件。此外，还讨论了用于稳健性分析的三种方法之间的关系：图像空间分析、向量优化和集值优化。最后，给出了一个寻找最短路径的应用，以验证本文推导结果的有效性。