An iterative working-set method for large-scale nonconvex quadratic programming

Nick Gould, Philippe Toint

Résultats de recherche: Contribution à un journal/une revueArticle

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Résumé

We consider a working-set method for solving large-scale quadratic programming problems for which there is no requirement that the objective function be convex. The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method used to solve the equality-constrained problem for this working set. A preconditioned conjugate gradient method is used for this inner iteration, with the preconditioner chosen especially to ensure feasibility of the iterates. The preconditioner is updated at the conclusion of each outer iteration to ensure that this feasibility requirement persists. The well-known equivalence between the conjugate-gradient and Lanczos methods is exploited when finding directions of negative curvature. Details of an implementation - the Fortran 90 package QPA in the forthcoming GALAHAD library - are given.
langue originaleAnglais
Pages (de - à)109-128
Nombre de pages20
journalApplied Numerical Mathematics
Volume43
Numéro de publication1-2
Les DOIs
étatPublié - 1 oct. 2002

Empreinte digitale

Nonconvex Quadratic Programming
Conjugate gradient method
Quadratic programming
Iterative methods
Preconditioner
Iteration
Lanczos Method
Preconditioned Conjugate Gradient Method
Negative Curvature
Requirements
Conjugate Gradient Method
Quadratic Programming
Iterate
Equality
Objective function
Equivalence

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An iterative working-set method for large-scale nonconvex quadratic programming. / Gould, Nick; Toint, Philippe.

Dans: Applied Numerical Mathematics, Vol 43, Numéro 1-2, 01.10.2002, p. 109-128.

Résultats de recherche: Contribution à un journal/une revueArticle

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