In this paper we consider the class of mathematical programs with complementarity constraints (MPCC). Under an appropriate constraint qualification of Mangasarian–Fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable C-stationary point for MPCC. Strong stability refers to the local uniqueness, existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed. This concept of strong stability was originally introduced by Kojima for standard nonlinear optimization; here, its generalization to MPCC demands a sophisticated technique which takes the disjunctive properties of the solution set of MPCC into account.

中文翻译：

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具有互补约束的数学程序的强稳定 C 平稳点

在本文中，我们考虑具有互补约束（MPCC）的数学程序类。在 Mangasarian-Fromovitz 类型的适当约束条件下，我们提出了 MPCC 强稳定 C 平稳点的拓扑和等效代数表征。强稳定性是指每个足够小的扰动问题的解的局部唯一性、存在性和连续依赖性，其中允许高达二阶的扰动。这种强稳定性的概念最初是小岛为标准非线性优化引入的；在这里，它对 MPCC 的推广需要一种复杂的技术，该技术考虑了 MPCC 解集的析取特性。