This article deals with a class of non-smooth mathematical programming with vanishing constraints. We introduce several kinds of constraint qualifications for these problems, and we study the relations between them. Then, we apply these constraint qualifications to obtain several stationary conditions. Finally, a sufficient condition for optimality of the problem is presented.

中文翻译：

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具有消失约束的Lipschitz优化问题的一阶最优性条件

本文讨论一类具有消失约束的非平滑数学编程。我们针对这些问题介绍了几种约束条件，并研究了它们之间的关系。然后，我们应用这些约束条件获得几个平稳条件。最后，给出了问题最优的充分条件。