A non-Lipschitz version of the Abadie constraint qualification is introduced for a nonsmooth and nonconvex general optimization problem. The relationship between the new Abadie-type constraint qualification and the local error bound property is clarified. Also, a necessary optimality condition, based on the pseudo-Jacobians, is derived under the Abadie constraint qualification. Moreover, some examples are given to illustrate the obtained results.

中文翻译：

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一般优化问题的一种新的 Abadie 型约束条件

针对非光滑和非凸一般优化问题引入了 Abadie 约束条件的非 Lipschitz 版本。阐明了新的 Abadie 类型约束条件与局部错误绑定属性之间的关系。此外，在 Abadie 约束条件下导出了一个基于伪雅可比的必要最优条件。此外，还给出了一些例子来说明得到的结果。