This paper is devoted to the study of nonsmooth mathematical programming problems with switching constraints in which all emerging functions are assumed to be locally Lipschitz. We introduce some Abadie type constraint qualifications which are based on the Mordukhovich subdifferential. Then, we investigate the interrelations between these constraint qualifications and derive several necessary stationary conditions at optimal solutions to the considered problems.

中文翻译：

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具有切换约束的非光滑优化中的平稳性

本文致力于研究具有切换约束的非光滑数学规划问题，其中所有新兴函数都假定为局部 Lipschitz。我们介绍了一些基于 Mordukhovich 次微分的 Abadie 类型约束条件。然后，我们研究这些约束条件之间的相互关系，并在所考虑的问题的最佳解决方案中推导出几个必要的平稳条件。