The CPLD Condition of Qi and Wei Implies the Quasinormality Constraint Qualification

The Constant Positive Linear Dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei and used for the analysis of SQP methods. In the paper where the CPLD was introduced, the authors conjectured that this condition could be a constraint qualification. This conjecture is proved in the present paper. Moreover, it will be shown that the CPLD condition implies the quasinormality constraint qualification, but the reciprocal is not true. Relations with other constraint qualifications will be given.