New Constraint Qualifications Based on the Decomposition of the Cone Defined by the Karush-Kuhn-Tucker Conditions.

In this paper, we introduce new constraint qualifications for optimization problems in Banach spaces. These are derived from a suitable decomposition of the cone associated with the Karush-Kuhn-Tucker (KKT) conditions into a linear subspace and a pointed cone. Based on this decomposition, we propose novel sequential (or asymptotic) constraint qualifications. Due to the geometric appeal of our new constraint qualifications, they fit naturally into general conic optimization problems and thus enhance the applicability of our approach. Furthermore, when applied to nonlinear optimization problems, the proposed qualifications are weaker than Robinson’s and other constant rank-type constraint qualifications commonly found in the literature, yet they remain strong enough to guarantee the validity of the error bound property, which plays a central role in sensitivity analysis and algorithmic convergence. All important statements are illustrated by examples.