This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric regularity of a multifunction in terms of quasidifferentials of the distance function to this multifunction. We also propose a new MFCQ-type constraint qualification for a parametric system of quasidifferentiable equality and inequality constraints and prove that it ensures the metric regularity of a multifunction associated with this system. As an application, we utilize our constraint qualification to strengthen existing optimality conditions for quasidifferentiable programming problems with equality and inequality constraints. We also prove the independence of the optimality conditions of the choice of quasidifferentials and present a simple example in which the optimality conditions in terms of quasidifferentials detect the non-optimality of a given point, while optimality conditions in terms of various subdifferentials fail to disqualify this point as non-optimal.

中文翻译：

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非光滑数学规划问题的拟可微映射的度量正则性和最优性条件

本文致力于根据Demyanov-Rubinov-Polyakova拟差分量分析度量规则性的必要条件和/或充分条件。根据距离函数到该函数的拟微分，我们获得了该函数的局部度量正则性的新的充要条件。我们还为准可区分的等式和不等式约束的参数系统提出了一种新的MFCQ型约束条件，并证明它可以确保与此系统关联的多功能系统的度量规则性。作为一种应用程序，我们利用约束条件限定条件来解决存在相等和不等式约束条件的拟可分编程问题的最优性条件。