LMI approximations for the radius of the intersection of ellipsoids: Survey

Authors
Henrion, D Tarbouriech, S Arzelier, D
Citation
D. Henrion et al., LMI approximations for the radius of the intersection of ellipsoids: Survey, J OPTIM TH, 108(1), 2001, pp. 1-28
Citations number
29
Categorie Soggetti
Engineering Mathematics
Journal title
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN journal
00223239 → ACNP
Volume
108
Issue
1
Year of publication
2001
Pages
1 - 28
Database
ISI
SICI code
0022-3239(200101)108:1<1:LAFTRO>2.0.ZU;2-8
Abstract
This paper surveys various linear matrix inequality relaxation techniques f or evaluating the maximum norm vector within the intersection of several el lipsoids. This difficult nonconvex optimization problem arises frequently i n robust control synthesis. Two randomized algorithms and several ellipsoid al approximations are described. Guaranteed approximation bounds are derive d in order to evaluate the quality of these relaxations.