On the constant positive linear dependence condition and its application to SQP methods

In this paper, we introduce a constant positive linear dependence condition ( CPLD), which is weaker than the Mangasarian-Fromovitz constraint qualifi cation ( MFCQ) and the constant rank constraint qualification (CRCQ). We sh ow that a limit point of a sequence of approximating Karush-Kuhn-Tucker (KK T) points is a KKT point if the CPLD holds there. We show that a KKT point satisfying the CPLD and the strong second-order sufficiency conditions (SSO SC) is an isolated KKT point. We then establish convergence of a general se quential quadratical programming (SQP) method under the CPLD and the SSOSC. Finally, we apply these results to analyze the feasible SQP method propose d by Panier and Tits in 1993 for inequality constrained optimization proble ms. We establish its global convergence under the SSOSC and a condition sli ghtly weaker than the Mangasarian-Fromovitz constraint qualification, and w e prove superlinear convergence of a modified version of this algorithm und er the SSOSC and a condition slightly weaker than the linear independence c onstraint qualification.