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

Title:
An iterative working-set method for large-scale nonconvex quadratic programming
Authors:
GOULD, Nicholas I. M, TOINT, Philippe L
Source:
19th Dundee biennial conference on numerical analysis, 26-29 June, 2001, Dundee, Scotland, UKApplied numerical mathematics. 43(1-2):109-128
Publisher Information:
Amsterdam: Elsevier, 2002.
Publication Year:
2002
Physical Description:
print, 42 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Programmation mathématique, Mathematical programming, Implémentation, Implementation, Ejecución, Méthode Lanczos, Lanczos method, Método Lanczos, Méthode algébrique, Algebraic method, Método algebraico, Méthode calcul, Computing method, Método cálculo, Méthode gradient conjugué, Conjugate gradient method, Método gradiente conjugado, Méthode itérative, Iterative method, Método iterativo, Point critique, Critical point, Punto crítico, Problème sélection, Selection problem, Problema selección, Programmation non convexe, Non convex programming, Programación no convexa, Programmation quadratique, Quadratic programming, Programación cuadrática, Préconditionnement, Preconditioning, Precondicionamiento, Résolution problème, Problem solving, Resolución problema, Simulation numérique, Numerical simulation, Simulación numérica, Structure grande échelle, Large scale structure, Estructura a gran escala, FORTRAN 90, Méthode ensemble actif, Active set method
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, United Kingdom
Department of Mathematics, Facultés Universitaires ND de la Paix, 61, rue de Bruxelles, 5000 Namur, Belgium
ISSN:
0168-9274
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=13935583
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Operational research. Management
Accession Number:
edscal.13935583
Database:
PASCAL Archive

Further Information

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.