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

Authors
Citation
Lq. Qi et Zx. Wei, On the constant positive linear dependence condition and its application to SQP methods, SIAM J OPTI, 10(4), 2000, pp. 963-981
Citations number
35
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON OPTIMIZATION
ISSN journal
10526234 → ACNP
Volume
10
Issue
4
Year of publication
2000
Pages
963 - 981
Database
ISI
SICI code
1052-6234(20000618)10:4<963:OTCPLD>2.0.ZU;2-D
Abstract
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.