A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification from Minchenko and Stakhovski that was called RCR. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCR and RCPLD with other known constraint qualifications, in particular, RCPLD is strictly weaker than CPLD and RCR, while still stronger than Abadie’s constraint qualification. We also verify that RCR is a strong second order constraint qualification.