Abstract

In this paper, we are concerned with a nonsmooth semivectorial bilevel optimization problem (P). Using a scalarization technique, we transform the lower-level problem into several scalar optimization problems $(P_{zx}^s).$ We give necessary optimality condition in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the special case where all functions are strictly differentiable.

中文翻译：

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非光滑半向量双层优化问题的最优性条件

摘要

在本文中，我们关注一个非光滑的半向量双层优化问题（P）。使用标量化技术，我们将下层问题转化为几个标量优化问题$（P_{žX}^s）。$我们根据极限次微分和极限法线锥给出了必要的最优性条件。然后，在所有函数严格可区分的特殊情况下，得出完全详细的一阶必要最优性条件。