Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 109-128 |
| Number of pages | 20 |
| Journal | Applied Numerical Mathematics |
| Volume | 43 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 1 Oct 2002 |
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An iterative working-set method for large-scale nonconvex quadratic programming. / Gould, Nick; Toint, Philippe.
In: Applied Numerical Mathematics, Vol. 43, No. 1-2, 01.10.2002, p. 109-128.Research output: Contribution to journal › Article
TY - JOUR
T1 - An iterative working-set method for large-scale nonconvex quadratic programming
AU - Gould, Nick
AU - Toint, Philippe
N1 - Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2002/10/1
Y1 - 2002/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0036776431&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(02)00120-4
DO - 10.1016/S0168-9274(02)00120-4
M3 - Article
AN - SCOPUS:0036776431
VL - 43
SP - 109
EP - 128
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 1-2
ER -