A Superlinearly Convergent Sequential Quadratically Constrained Quadratic Programming Algorithm for Degenerate Nonlinear Programming

We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian--Fromovitz constraint qualification and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorit...

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Veröffentlicht in:SIAM journal on optimization Jg. 12; H. 4; S. 949 - 978
1. Verfasser: Anitescu, Mihai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 2002
Schlagworte:
Algorithms
Applied mathematics
Approximation
Lagrange multiplier
Neighborhoods
Optimization
Quadratic programming
ISSN:1052-6234, 1095-7189
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Zusammenfassung:We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian--Fromovitz constraint qualification and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorithm solves a succession of subproblems that have quadratic objectives and quadratic constraints, both possibly nonconvex. By the use of a trust-region constraint we guarantee that any stationary point of the subproblem induces superlinear convergence, which avoids the problem of computing a global minimum. We compare this algorithm with sequential quadratic programming algorithms on several degenerate nonlinear programs.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623499365309