Characterization of Strong Stability for C-stationary Points in MPCC

Jongen, Hubertus Th.;Shikhman, Vladimir;Steffensen, Sonja
(2012) Mathematical Programming — Vol. 132, n° 1-2, p. 295-308 (2012)

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Authors
  • Jongen, Hubertus Th.RWTH Aachen University
    Author
  • Shikhman, VladimirUCLouvain
    Author
  • Steffensen, SonjaRWTH Aachen University
    Author
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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Jongen, H. Th., Shikhman, V., & Steffensen, S. (2012). Characterization of Strong Stability for C-stationary Points in MPCC. Mathematical Programming, 132(1-2), 295-308. https://doi.org/10.1007/s10107-010-0396-0 (Original work published 2012)