DOI: 10.1017/s0962492901000071. Semidefinite optimization

10.1017/s0962492901000071

Crossref journal-article

Cambridge University Press (CUP)

Acta Numerica (56)

Abstract

Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds for hard combinatorial optimization problems. Part also derives from great advances in our ability to solve such problems efficiently in theory and in practice (perhaps ‘or’ would be more appropriate: the most effective computational methods are not always provably efficient in theory, and vice versa). Here we describe this class of optimization problems, give a number of examples demonstrating its significance, outline its duality theory, and discuss algorithms for solving such problems.

Bibliography

Todd, M. J. (2001). Semidefinite optimization. Acta Numerica, 10, 515â560.

Authors 1

M. J. Todd (first)

References 0 Referenced 313

None

Dates

Type	When
Created	17 years ago (July 25, 2008, 12:44 a.m.)
Deposited	6 years, 2 months ago (June 6, 2019, 4:04 p.m.)
Indexed	1 month, 1 week ago (July 13, 2025, 10:54 p.m.)
Issued	24 years, 3 months ago (May 1, 2001)
Published	24 years, 3 months ago (May 1, 2001)
Published Online	22 years, 7 months ago (Jan. 9, 2003)
Published Print	24 years, 3 months ago (May 1, 2001)

Funders 0

None

BibTeX

@article{Todd_2001, title={Semidefinite optimization}, volume={10}, ISSN={1474-0508}, url={http://dx.doi.org/10.1017/s0962492901000071}, DOI={10.1017/s0962492901000071}, journal={Acta Numerica}, publisher={Cambridge University Press (CUP)}, author={Todd, M. J.}, year={2001}, month=may, pages={515–560} }

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