This paper is devoted to the study of the metric subregularity constraint qualification for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and quasi-normality, recently introduced by Bai et al., which combine the standard approach via pseudo- and quasi-normality with modern tools of directional variational analysis. We focus on applications to disjunctive programs, where (directional) pseudo-normality is characterized via an extremal condition. This, in turn, yields efficient tools to verify pseudo-normality and the metric subregularity constraint qualification, which include, but are not limited to, Robinson’s result on polyhedral multifunctions and Gfrerer’s second-order sufficient condition for metric subregularity. Finally, we refine our study by defining the new class of ortho-disjunctive programs which comprises prominent optimization problems such as mathematical programs with complementarity, vanishing or switching constraints.

本文致力于一般优化问题的度量次规则约束条件的研究，重点是非凸设置。我们详细阐述了Bai等人最近提出的定向伪准和准正态性概念，该方法将通过伪准和准正态性的标准方法与定向变分分析的现代工具相结合。我们专注于析取程序的应用，其中（定向）伪正态通过极值条件来表征。反过来，这提供了验证伪正态性和度量次正则性约束条件的有效工具，包括但不限于罗宾逊关于多面体函数和Gfrerer的结果。度量次规则性的二阶充分条件。最后，我们通过定义一类新的正交分离程序来完善我们的研究，该程序包括突出的优化问题，例如具有互补性，消失或切换约束的数学程序。