LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future

Victor Vinnikov

doi:10.1007/978-3-0348-0411-0_23

LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future

Victor Vinnikov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Abstract

10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions and some new results.

Original language	English
Title of host publication	Mathematical Methods in Systems, Optimization, and Control
Subtitle of host publication	Festschrift in Honor of J. William Helton
Editors	H. Dym, M. de Oliveira, M. Putinar
Publisher	Birkhäuser Basel
Pages	325-349
ISBN (Electronic)	9783034804110
ISBN (Print)	9783034804103
DOIs	https://doi.org/10.1007/978-3-0348-0411-0_23
State	Published - 10 May 2012

Publication series

Name	Operator Theory: Advances and Applications
Volume	222
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Keywords

math.OC
Primary: 14M12, 90C22, Secondary: 14P10, 52A20

Access to Document

10.1007/978-3-0348-0411-0_23

Cite this

Vinnikov, V. (2012). LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future. In H. Dym, M. de Oliveira, & M. Putinar (Eds.), Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton (pp. 325-349). (Operator Theory: Advances and Applications; Vol. 222). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-0411-0_23

Vinnikov, Victor. / LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces : Past, Present, and Future. Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton. editor / H. Dym ; M. de Oliveira ; M. Putinar . Birkhäuser Basel, 2012. pp. 325-349 (Operator Theory: Advances and Applications).

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abstract = "10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions and some new results. ",

keywords = "math.OC, Primary: 14M12, 90C22, Secondary: 14P10, 52A20",

author = "Victor Vinnikov",

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doi = "10.1007/978-3-0348-0411-0_23",

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series = "Operator Theory: Advances and Applications",

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booktitle = "Mathematical Methods in Systems, Optimization, and Control",

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Vinnikov, V 2012, LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future. in H Dym, M de Oliveira & M Putinar (eds), Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton. Operator Theory: Advances and Applications, vol. 222, Birkhäuser Basel, pp. 325-349. https://doi.org/10.1007/978-3-0348-0411-0_23

LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future. / Vinnikov, Victor.
Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton. ed. / H. Dym; M. de Oliveira; M. Putinar . Birkhäuser Basel, 2012. p. 325-349 (Operator Theory: Advances and Applications; Vol. 222).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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T2 - Past, Present, and Future

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AB - 10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions and some new results.

KW - math.OC

KW - Primary: 14M12, 90C22, Secondary: 14P10, 52A20

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DO - 10.1007/978-3-0348-0411-0_23

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BT - Mathematical Methods in Systems, Optimization, and Control

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Vinnikov V. LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future. In Dym H, de Oliveira M, Putinar M, editors, Mathematical Methods in Systems, Optimization, and Control: Festschrift in Honor of J. William Helton. Birkhäuser Basel. 2012. p. 325-349. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0411-0_23

LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future

Abstract

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Keywords

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