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Mathematical Methods in Systems, Optimization, and Control pp 325–349Cite as

Birkhäuser

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

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 222))

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.

Mathematics Subject Classification. Primary: 14M12, 90C22; secondary: 14P10, 52A20.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel, 84105

    Victor Vinnikov

Authors
  1. Victor Vinnikov
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Corresponding author

Correspondence to Victor Vinnikov .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Harry Dym

  2. , Department of Mechanical and, University of California San Diego, Gilman Drive 9500, La Jolla, 92093-0411, California, USA

    Mauricio C. de Oliveira

  3. College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, 93106, California, USA

    Mihai Putinar

Additional information

To Bill Helton, on the occasion of his 65th birthday

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

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