On estimating the regular normal cone to constraint systems and stationarity conditions

Abstract

Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than M-stationarity. We apply our theory to three classes of mathematical programs frequently arising in the literature.

Keywords:

• Regular normal cone
• B-
• M-
• S-stationarity
• complementarity constraints
• vanishing constraints
• generalized equations

Acknowledgements

The authors would like to express their gratitude to the reviewers for their careful reading and numerous important suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by the Austrian Science Fund (FWF) [grant number P26132-N25].