In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019. https://doi.org/10.1007/s11117-019-00685-1) is erroneous. Using techniques from variational analysis, we propose other proofs to detect necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first order necessary optimality conditions are then given in the smooth setting while using the generalized differentiation calculus of Mordukhovich.

中文翻译：

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使用kth目标加权约束方法的半向量双层优化问题的必要最优性条件

在本文中，我们指出了最近一篇论文中的定理11的证明（Lafhim in Positivity，2019.https：//doi.org/10.1007/s11117-019-00685-1）是错误的。利用变分分析技术，我们提出了其他证明，以根据Karush–Kuhn–Tucker乘数检测必要的最优条件。我们的主要结果是根据极限次微分和极限法线锥给出的。然后，使用Mordukhovich的广义微分演算，在光滑的环境中给出完全详细的一阶必要最优条件。