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The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope.
On the Shannon capacity of a graph
László Lovász · 1979
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Cones of matrices and set-functions and 0 0 - 1 1 optimization
László Lovász and Alexander Schrijver · 1991
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Expressing combinatorial optimization problems by linear programs
Mihalis Yannakakis · 1991
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Ideals, Varieties and Algorithms
David Cox, John Little, and Donal O’Shea · 1992
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Geometric algorithms and combinatorial optimization
Martin Grötschel, László Lovász, and Alexander Schrijver · 1993
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Convex Polytopes
Branko Grünbaum · 2003
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The strong perfect graph theorem
Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas · 2006
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Theta bodies for polynomial ideals
João Gouveia, Pablo A. Parrilo, and Rekha R. Thomas · 2010
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Constructing extended formulations from reflection relations
Volker Kaibel and Kanstantsin Pashkovich · 2011
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Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary, and Ronald de Wolf · 2012
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Smallest compact formulation for the permutahedron
Michel Goemans
Cited in the paper.
Macaulay 2, a software system for research in algebraic geometry
Daniel R. Grayson and Michael E. Stillman
Cited in the paper.
Extended formulations for polygons
Samuel Fiorini, Thomas Rothvoss, and Hans Raj Tiwary · 2012
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On the geometric interpretation of the nonnegative rank
Nicolas Gillis and Francois Glineur · 2012
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Combinatorial bounds on nonnegative rank and extended formulations
Samuel Fiorini, Volker Kaibel, Kanstantsin Pashkovich, and Dirk O. Theis · 2013
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Lifts of convex sets and cone factorizations
João Gouveia, Pablo Parrilo, and Rekha Thomas · 2013
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