The DOI matches its Crossref record; 29 of the 29 references it cites were found in a registry or an index.
A Survey of the S-Lemma
Abstract
In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry, and linear algebra as well. These were all active research areas, but as there was little interaction between researchers in these different areas, their results remained mainly isolated. Here we give a unified analysis of the theory by providing three different proofs for the S-lemma and revealing hidden connections with various areas of mathematics. We prove some new duality results and present applications from control theory, error estimation, and computational geometry.
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Linear Matrix Inequalities in System and Control Theory
Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970777 · Cited by 21,687
Ridge regression: Biased estimation for nonorthogonal problems
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Ridge Regression: Biased Estimation for Nonorthogonal Problems
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Cited by
Fisher, A., Rudin, C., & Dominici, F. (2018) · arXiv · doi:10.48550/arxiv.1801.01489 · Cited by 1,165
Theory and applications of robust optimization
Bertsimas, D., Brown, D. B., & Caramanis, C. (2011) · SIAM Review · doi:10.1137/080734510 · Cited by 134
Metadata
- Authors
- Pólik, I., & Terlaky, T.
- Venue
- SIAM Review
- Published
- 2007-01
- Volume
- 49
- Issue
- 3
- Pages
- 371-418
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2140214428
- Cited by
- 499
- References
- 29
- FWCI
- 15.85
- Type
- journal article
- Language
- en
- Open access
- closed
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