TY - JOUR
T1 - A multilevel algorithm for solving the trust-region subproblem
AU - Toint, Philippe
AU - Tomanos, D.
AU - Weber Mendonca, Melissa
N1 - Publication code : FP SB010/2007/04 ; QA 0002.2/001/07/04
PY - 2009/4/1
Y1 - 2009/4/1
N2 - We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest level (corresponding to the finest discretization), but information on the problem curvature at lower levels is exploited for improved efficiency. The algorithm is inspired by the method described in [J.J. More and D.C. Sorensen, On the use of directions of negative curvature in a modified Newton method, Math. Program. 16(1) (1979), pp. 1-20], for which two different multilevel variants will be analysed. Some preliminary numerical comparisons are also presented. © 2009 Taylor & Francis.
AB - We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest level (corresponding to the finest discretization), but information on the problem curvature at lower levels is exploited for improved efficiency. The algorithm is inspired by the method described in [J.J. More and D.C. Sorensen, On the use of directions of negative curvature in a modified Newton method, Math. Program. 16(1) (1979), pp. 1-20], for which two different multilevel variants will be analysed. Some preliminary numerical comparisons are also presented. © 2009 Taylor & Francis.
UR - http://www.scopus.com/inward/record.url?scp=61349197442&partnerID=8YFLogxK
U2 - 10.1080/10556780802571467
DO - 10.1080/10556780802571467
M3 - Article
VL - 24
SP - 299
EP - 311
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 2
ER -