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

Liqun Qi, Zengxin Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

121 Citations (Scopus)

Abstract

In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush-Kuhn-Tucker (KKT) 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 (SSOSC) is an isolated KKT point. We then establish convergence of a general sequential quadratical programming (SQP) method under the CPLD and the SSOSC. Finally, we apply these results to analyze the feasible SQP method proposed by Panier and Tits in 1993 for inequality constrained optimization problems. We establish its global convergence under the SSOSC and a condition slightly weaker than the Mangasarian-Fromovitz constraint qualification, and we prove superlinear convergence of a modified version of this algorithm under the SSOSC and a condition slightly weaker than the linear independence constraint qualification.
Original languageEnglish
Pages (from-to)963-981
Number of pages19
JournalSIAM Journal on Optimization
Volume10
Issue number4
DOIs
Publication statusPublished - 1 Jan 2000
Externally publishedYes

Keywords

  • Constrained optimization
  • Constraint qualification
  • Feasible SQP method
  • Global convergence
  • KKT point
  • Superlinear convergence

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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