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

Ben-Gurion University of the Negev

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

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	American 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
Pages	325-349
ISBN (Electronic)	9783034804110
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

Keywords

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

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). 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. 2012. pp. 325-349 (Operator Theory: Advances and Applications).

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

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

author = "Victor Vinnikov",

year = "2012",

month = may,

day = "10",

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

language = "American English",

isbn = "9783034804103",

series = "Operator Theory: Advances and Applications",

pages = "325--349",

editor = "H. Dym and {de Oliveira}, M. and M. Putinar",

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, 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. 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

AU - Vinnikov, Victor

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

KW - math.OC

U2 - 10.1007/978-3-0348-0411-0_23

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

M3 - Chapter

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BT - Mathematical Methods in Systems, Optimization, and Control

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ER -

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. 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

Publication series

Keywords

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Cite this