Polynomial complexity for a Nesterov-Todd potential-reduction method with inexact search directions

Author

Gillberg, Jonas ; Hansson, Anders

Author_Institution

Dept. of Electr. Eng., Linkoping Univ., Sweden

Volume

4

fYear

2003

fDate

9-12 Dec. 2003

Firstpage

3824

Abstract

In this paper is discussed how to efficiently solve semidefinite programs related to the Kalman-Yakubovich-Popov lemma. We consider a potential-reduction method where Nesterov-Todd search directions are computed inexactly by applying a preconditioned conjugate gradient method to the Schur complement equation. An efficient preconditioner based on Lyapunov equations is derived. We give a proof of polynomial convergence for this interior point method.

Keywords

Lyapunov matrix equations; Popov criterion; conjugate gradient methods; convergence of numerical methods; mathematical programming; polynomials; Kalman-Yakubovich-Popov lemma; Lyapunov equations; Nesterov-Todd potential reduction method; Nesterov-Todd search directions; Schur complement equation; conjugate gradient method; inexact search directions; interior point method; polynomial complexity; polynomial convergence; semidefinite programs; Artificial intelligence; Automatic control; Control nonlinearities; Convergence; Gradient methods; Integral equations; Nonlinear equations; Polynomials; Robust control; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7924-1

Type

conf

DOI

10.1109/CDC.2003.1271745

Filename

1271745