Optimizing eigenvalues of symmetric definite pencils

Jean Pierre A Haeberly, Michael L. Overton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the following quasiconvex optimization problem: minimize the largest eigenvalue of a symmetric definite matrix pencil depending on parameters. A new form of optimality conditions is given, emphasizing a complementarity condition on primal and dual matrices. Newton's method is then applied to these conditions to give a new quadratically convergent interior-point method which works well in practice. The algorithm is closely related to primal-dual interior-point methods for semidefinite programming.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
PublisherAmerican Automatic Control Council
Pages836-839
Number of pages4
Volume1
StatePublished - 1994
EventProceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA
Duration: Jun 29 1994Jul 1 1994

Other

OtherProceedings of the 1994 American Control Conference. Part 1 (of 3)
CityBaltimore, MD, USA
Period6/29/947/1/94

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Newton-Raphson method

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Haeberly, J. P. A., & Overton, M. L. (1994). Optimizing eigenvalues of symmetric definite pencils. In Proceedings of the American Control Conference (Vol. 1, pp. 836-839). American Automatic Control Council.

Optimizing eigenvalues of symmetric definite pencils. / Haeberly, Jean Pierre A; Overton, Michael L.

Proceedings of the American Control Conference. Vol. 1 American Automatic Control Council, 1994. p. 836-839.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Haeberly, JPA & Overton, ML 1994, Optimizing eigenvalues of symmetric definite pencils. in Proceedings of the American Control Conference. vol. 1, American Automatic Control Council, pp. 836-839, Proceedings of the 1994 American Control Conference. Part 1 (of 3), Baltimore, MD, USA, 6/29/94.
Haeberly JPA, Overton ML. Optimizing eigenvalues of symmetric definite pencils. In Proceedings of the American Control Conference. Vol. 1. American Automatic Control Council. 1994. p. 836-839
Haeberly, Jean Pierre A ; Overton, Michael L. / Optimizing eigenvalues of symmetric definite pencils. Proceedings of the American Control Conference. Vol. 1 American Automatic Control Council, 1994. pp. 836-839
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