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

By Victor Vinnikov. 2012

82 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/600235e51556aa3620e7939d03431e986ab3ed0e

Citations in the corpus

• Unimodality, log-concavity, real-rootedness and beyond (2015, unknown): “nverse of Proposition 9.1 holds, see Theorem 7.4. The analog of Theorem 7.4 for n3 fails to be true by a simple count of parameters. For possible partial converses of Proposition 9.1, see the survey [100]. 28 PETTER BRAND EN Recently attempts have been made to nd appropriate multivariate analogs of ”