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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Vydáno v:SIAM journal on optimization Ročník 12; číslo 4; s. 949 - 978
Hlavní autor: Anitescu, Mihai
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 2002
Témata:
Algorithms
Applied mathematics
Approximation
Lagrange multiplier
Neighborhoods
Optimization
Quadratic programming
ISSN:1052-6234, 1095-7189
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623499365309