Abstract
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.
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Günzel, H., Hernández Escobar, D. & Rückmann, JJ. MPCC: Strong Stability of M-stationary Points. Set-Valued Var. Anal 29, 645–659 (2021). https://doi.org/10.1007/s11228-021-00592-2
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DOI: https://doi.org/10.1007/s11228-021-00592-2
Keywords
- Mathematical programs with complementarity constraint
- M-stationarity
- Strong stability
- Algebraic characterization
- MPCC-LICQ