A bundle method for efficiently solving large structured linear matrix inequalities

Author

Miller, Scott A. ; Smith, Roy S.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

2

fYear

2000

fDate

2000

Firstpage

1405

Abstract

An algorithm is proposed for solving large LMI feasibility problems, which exploits the structure of the LMI and avoids forming and manipulating large matrices. It is derived from the spectral bundle method of Helmberg and Rendl (1997), but modified to properly handle inexact eigenvalues and eigenvectors obtained from Lanczos iterations. The complexity is estimated from numerical experiments and it compares favorably with structured interior-point methods; moreover, this approach applies to more general structures

Keywords

Hilbert spaces; computational complexity; convergence; eigenvalues and eigenfunctions; function approximation; matrix algebra; Lanczos iterations; feasibility problems; inexact eigenvalues; inexact eigenvectors; large structured linear matrix inequalities; spectral bundle method; structured interior-point methods; Algorithm design and analysis; Costs; Eigenvalues and eigenfunctions; Iterative methods; Linear matrix inequalities; Linear systems; Polynomials; Sparse matrices; Symmetric matrices; Time domain analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2000. Proceedings of the 2000

Conference_Location

Chicago, IL

ISSN

0743-1619

Print_ISBN

0-7803-5519-9

Type

conf

DOI

10.1109/ACC.2000.876732

Filename

876732