Summary: The Constant Positive Linear Dependence condition of Qi
and Wei implies the quasinormality constraint qualification
J. M. Mart´inez
M. L. Schuverdt
April 15, 2004.
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. Re-
lations with other constraint qualifications will be given.
Key words: Nonlinear Programming, Constraint Qualifications, CPLD condi-
A constraint qualification is a property of feasible points of nonlinear programming prob-
lems that, when satisfied by a local minimizer, guarantees that the Karush-Kuhn-Tucker
(KKT) conditions take place at that point. See, for example, [1, 2]. When a constraint