Set-Valued and Variational Analysis ( IF 1.3 ) Pub Date : 2021-06-08 , DOI: 10.1007/s11228-021-00592-2 Harald Günzel , Daniel Hernández Escobar , Jan-J. Rückmann
In this paper we study the class of mathematical programs with complementarity constraints MPCC. Under the Linear Independence constraint qualification MPCC-LICQ we state a topological as well as an equivalent algebraic characterization for the strong stability (in the sense of Kojima) of an M-stationary point for MPCC. By allowing perturbations of the describing functions up to second order, the concept of strong stability refers here to the local existence and uniqueness of an M-stationary point for any sufficiently small perturbed problem where this unique solution depends continuously on the perturbation. Finally, some relations to S- and C-stationarity are briefly discussed.
中文翻译:
MPCC:M-静止点的强稳定性
在本文中,我们研究了一类具有互补约束 MPCC 的数学程序。在线性独立约束条件 MPCC-LICQ 下,我们陈述了 MPCC 的 M 平稳点的强稳定性(在 Kojima 的意义上)的拓扑以及等效的代数特征。通过允许描述函数的扰动达到二阶,强稳定性的概念在这里指的是对于任何足够小的扰动问题的 M 平稳点的局部存在和唯一性,其中这个唯一的解决方案持续依赖于扰动。最后,简要讨论了与 S 和 C 平稳性的一些关系。