MPCC: Strong stability of M-stationary points
Journal article, Peer reviewed
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OriginalversjonSet-Valued and Variational Analysis. 2021, 29 (3), 645-659. https://doi.org/10.1007/s11228-021-00592-2
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.