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.
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