We study the implications of a well-known metric inequality condition on sets to the applicability of standard necessary optimality conditions for constrained optimization problems when a new constraint is added. We compare this condition with several other constraint qualification conditions in the literature, and due to its metric nature, we apply it to nonsmooth optimization problems in order to perform first a penalization and then to give optimality conditions in terms of generalized differentiability.

中文翻译：

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集上的度量不等式条件和优化结果

我们研究了一个众所周知的度量不等式对集合的影响，当添加新的约束时，该条件对约束优化问题的标准必要最优性条件的适用性。我们将此条件与文献中的其他几个约束限定条件进行比较，并且由于其度量性质，我们将其应用于非平滑优化问题，以便首先进行惩罚，然后根据广义可微性给出最优性条件。