A note on stability of stationary points in mathematical programs with generalized complementarity constraints

Abstract

We consider parameter-dependent mathematical programs with constraints governed by the generalized non-linear complementarity problem and with additional non-equilibrial constraints. We study a local behaviour of stationarity maps that assign the respective C- or M-stationarity points of the problem to the parameter. Using generalized differential calculus rules, we provide criteria for the isolated calmness and the Aubin properties of stationarity maps considered. To this end, we derive and apply formulas of some particular objects of the third-order variational analysis.

Keywords:

• parameter-dependent mathematical programs with generalized equilibrium constraints
• M-stationarity
• C-stationarity
• isolated calmness
• Aubin property

AMS Subject Classifications:

• 90C31
• 90C33
• 49K40

Acknowledgements

The author would like to thank both referees for their very detailed comments which helped to improve the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Grant Agency of the Czech Republic [grant number P402/12/1309].