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  A Book on Linear Matrix Inequalities          
 
 
Russian

Study of Linear Matrix Inequalities. A Software Companion.

Alexander N. Churilov and Alina V. Gessen.

St. Petersburg University Press, St. Petersburg, 2004. 148 pp.
(In Russian.)

ISBN 5-288-03597-0

The site of the publishers: Unipress .

Order and delivery: post@unipress.ru .


Abstract
The book written in Russian presents an overview of software for study of optimization problems referred to linear matrix inequalities, and a guide to the programme packages LMILab, LMITOOL, SeDuMi Interface, YALMIP, and KYPD. The book is intended for users of MATLAB and Scilab, who are interested in applications of linear matrix inequalities to control theory, mechanics, and other fields. They get a powerful tool for their investigations without going into mathematical details. The presentation is accompanied by a great number of sample programmes.

Contents
Preface

1. General information
1.1. The settings of problems for study of LMIs
1.2. Non-strict LMIs
1.3. Duality
1.4. Numerical methods for study of LMIs
1.5. Matrix variables
1.6. Schur complement
1.7. Examples
1.8. S-procedure
1.9. Solvers and parsers
1.10. An overview of parsers for study of LMIs
1.11. A history of LMIs in control theory

2. LMILab package
2.1. Definition of a system of LMIs
2.2. Getting information on a system
2.3. Mutual transformations of matrix and design variables
2.4. Investigation of LMIs
2.5. Estimation of LMIs
2.6. Modification of LMIs
2.7. Examples

3. LMITOOL package
3.1. Review of the package
3.2. Functions of the package
3.3. Examples
3.4. LMITOOL in MATLAB

4. SeDuMi Interface package
4.1. Review of the package
4.2. Definition of an optimization problem
4.3. Solving an optimization problem
4.4. Modification of a problem
4.5. Getting information on a problem
4.6. Examples

5. YALMIP package
5.1. Review of the package
5.2. Definition of matrix variables
5.3. Definition of constraints
5.4. Solving a problem of semi-definite programming
5.5. Examples
5.6. A study of bilinear matrix inequalities
5.7. Auxiliary commands

6. KYPD package
6.1. Review of the package
6.2. Main functions
6.3. A work with KYPD in YALMIP

Appendix 1
Appendix 2
References
Index of commands and functions


Sites of the main programme packages related to LMI
Parsers and parsers joint with solvers:
LMILab (documentation)
Since MATLAB Release 14, LMILab is a part of Robust Control Toolbox.
LMITOOL (Scilab version)
LMITOOL is incorporated into Scilab.
YALMIP
CVX
SeDuMi Interface
SDPSOL
KYPD
xLMI
LMILab Translator
Solvers:
SeDuMi
CSDP
DSDP
PENSDP, PENBMI
SDPA
SDPT3
SDPLR
LMIRank
SBmethod
Packages not related to LMI, but close in subject:
SOSTOOLS
IQC toolbox
GloptyPoly
RoMulOC
PoLyX
MOSEK
General sites on LMI and SDP:
Site of Stephen Boyd's research team
Semidefinite Programming (H. Wolkowicz)
Semidefinite Programming (Ch. Helmberg)
SDP Page (F. Alizadeh)
Interior-Point Methods Online (S. Wright, before 2001)
Optimization Online: Linear, Cone and Semidefinite Programming
NEOS Solvers
Semidefinite Programming Packages
 
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Last Modified: April 15, 2008