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Characterization of strong stability for C-stationary points in MPCC

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Abstract

We study mathematical programs with complementarity constraints (MPCC). Special focus will be on C-stationary points. Under the Linear Independence Constraint Qualification we characterize strong stability of C-stationary points (in the sense of Kojima) by means of first and second order information of the defining functions. It turns out that strong stability of C-stationary points allows a possible degeneracy of bi-active Lagrange multipliers. Some relations to other stationarity concepts (such as A-, M-, S- and B-stationarity) are shortly discussed.

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Correspondence to V. Shikhman.

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Jongen, H.T., Shikhman, V. & Steffensen, S. Characterization of strong stability for C-stationary points in MPCC. Math. Program. 132, 295–308 (2012). https://doi.org/10.1007/s10107-010-0396-0

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  • DOI: https://doi.org/10.1007/s10107-010-0396-0

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