Second-Order Enhanced Optimality Conditions and Constraint Qualifications

In this paper, we study second-order necessary optimality conditions for smooth nonlinear programming problems. Employing the second-order variational analysis and generalized differentiation, under the weak constant rank (WCR) condition, we derive an enhanced version of the classical weak second-order Fritz–John condition which contains some new information on multipliers. Based on this enhanced weak second-order Fritz–John condition, we introduce the weak second-order enhanced Karush–Kuhn–Tucker condition and propose some associated second-order constraint qualifications. Finally, using our new second-order constraint qualifications, we establish new sufficient conditions for the existence of a Hölder error bound condition.