On relaxed constant rank regularity condition in mathematical programming

Abstract

Regularity conditions or constraint qualifications play an important role in mathematical programming. In this article we present a relaxed version of the constant rank constraint qualification (CRCQ) which is weaker than the original CRCQ for mixed-constrained non-linear programming problems and is still a regularity condition. The main aim of this article is to show that the relaxed CRCQ (and, consequently, CRCQ too) implies the R-regularity (in other terms the error bound property) of a system of inequalities and equalities. In the same way we prove that the constant positive linear dependence (CPLD) condition also implies R-regularity.

Keywords:

• non-linear programming
• regularity conditions
• constraint qualifications
• error bounds
• Lagrange multipliers

AMS Subject Classifications::

• 41A50
• 49K40
• 90C31

Acknowledgement

The authors are indebted to the referees of the article for their useful comments.