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

被引：31

作者：

Henrion, D ^{[1
]}

Tarbouriech, S ^{[1
]}

Arzelier, D ^{[1
]}

机构：

[1] CNRS, Lab Anal & Architecture Syst, Toulouse, France

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2001年 / 108卷 / 01期

关键词：

linear matrix inequalities; nonconvex optimization; convex relaxations; ellipsoids; robust control;

D O I：

10.1023/A:1026454804250

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 [运筹学与控制论]; 12 [管理学]; 1201 [管理科学与工程]; 1202 [工商管理学]; 120202 [企业管理];

摘要：

This paper surveys various linear matrix inequality relaxation techniques for evaluating the maximum norm vector within the intersection of several ellipsoids. This difficult nonconvex optimization problem arises frequently in robust control synthesis. Two randomized algorithms and several ellipsoidal approximations are described. Guaranteed approximation bounds are derived in order to evaluate the quality of these relaxations.

引用

页码：1 / 28

页数：28

共 30 条

[1]

[Anonymous], 1995, MATLAB LMI CONTROL T

[2]

BALAKRISHNAN V, 1991, GLOBAL OPTIMIZATION

[3]

Robust convex optimization [J].