Strong Stability of degenerated C–stationary points in MPCC

Daniel Hernandez Escobar, Daniel Hernandez Escobar, Jan-Joachim Rückmann

We consider Mathematical Programs with Complementarity Constraints (MPCC). The study of strong stability of C-stationary points plays a relevant role in sensitivity analysis and parametric optimization. In 2010, H. Jongen et al. characterized the strong stability of C-stationary points for MPCC under the assumption that the Linear Independence Constraint Qualification (LICQ) holds.
Here, we focus on the characterization of strong stability of C-stationary points when LICQ does not hold. We provide an upper bound on the number of constraints as a necessary condition for strong stability as well as a lower bound when a Mangasarian-Fromovitz-type constraint qualification does not hold. We introduce a weaker constraint qualification which turned out to be necessary for strong stability.