On the relation between constant positive linear dependence condition and quasinormality constraint qualification

The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors conjectured that the CPLD could be a constraint qualification. This conjecture is proven in the present paper. Moreover, it is shown that the CPLD condition implies the quasinormality constraint quali. cation, but that the reciprocal is not true. Relations with other constraint quali. cations are given.