Relation between the constant rank and the relaxed constant rank constraint qualifications

Abstract

This article discusses a relation between the constant rank constraint qualification (CRCQ) and the recently proposed relaxed constant rank constraint qualification (RCRCQ). We show that a parametric constraint system satisfying the RCRCQ is locally diffeomorphic to a system satisfying the CRCQ. We use this result to extend some existing results for the CRCQ to the RCRCQ, establish a relation between the RCRCQ and the Mangasarian–Fromovitz constraint qualification, and obtain a weakened version of the Aubin property under the RCRCQ.

Keywords:

• constraint qualification
• constant rank
• error bound
• Aubin property

AMS Subject Classiffications::

• 90C30
• 90C31
• 49J53
• 54C60

Acknowledgements

This material is based upon research supported by the National Science Foundation under Grant DMS-0807893. The author thanks Prof Alexey Izmailov for raising a question that has inspired the work, and for very helpful discussion on the material presented here. The author also thanks two anonymous referees for comments that have greatly improved this article.