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Let M be a p-by-q matrix with nonnegative entries.
Mathematical description of linear dynamical systems
R. E. Kalman · 1963
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Computers and Intractability: A guide to the theory of NP-completeness
M. R. Garey and D. S. Johnson · 1979
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Principal component analysis in linear systems: Controllability, observability, and model reduction
B. Moore · 1981
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Expressing combinatorial optimization problems by linear programs
M. Yannakakis · 1991
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On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals
J. Renegar · 1992
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Nonnegative ranks, decompositions, and factorizations of nonnegative matrices
J.E. Cohen and U.G. Rothblum · 1993
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Semidefinite programming
L. Vandenberghe and S. Boyd · 1996
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On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues
G. Pataki · 1998
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Learning the parts of objects by non-negative matrix factorization
D. D. Lee and H. S. Seung · 1999
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A remark on the rank of positive semidefinite matrices subject to affine constraints
A. Barvinok · 2001
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Principal component analysis
I. Jolliffe · 2002
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Completely Positive Matrices
A. Berman and N. Shaked-Monderer · 2003
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Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
D. Mond, J. Smith, and D. van Straten · 2003
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Convex Optimization
S.P. Boyd and L. Vandenberghe · 2004
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Hyperbolic programs, and their derivative relaxations
J. Renegar · 2006
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Complexity measures of sign matrices
N. Linial, S. Mendelson, G. Schechtman, and A. Shraibman · 2007
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Testing the dimension of Hilbert spaces
N. Brunner, S. Pironio, A. Acin, N. Gisin, A.A. Méthot, and V. Scarani · 2008
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Lower bound on the dimension of a quantum system given measured data
S. Wehner, M. Christandl, and A.C. Doherty · 2008
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Lower bounds in communication complexity based on factorization norms
N. Linial and A. Shraibman · 2009
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On the complexity of nonnegative matrix factorization
S. A. Vavasis · 2009
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Copositive programming–a survey
M. Dür · 2010
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On the nonnegative rank of distance matrices
P. Hrubeš · 2012
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Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
T. Lee and D. O. Theis · 2012
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Semidefinite representation for convex hulls of real algebraic curves
C. Scheiderer · 2012
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On the existence of 0/1 polytopes with high semidefinite extension complexity
J. Briët, D. Dadush, and S. Pokutta · 2013
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Combinatorial bounds on nonnegative rank and extended formulations
S. Fiorini, V. Kaibel, K. Pashkovich, and D. O. Theis · 2013
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Lifts of convex sets and cone factorizations
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P.E. Frenkel and M. Weiner · 2010
Cited alongside, same era.
The algebraic degree of semidefinite programming
J. Nie, K. Ranestad, and B. Sturmfels · 2010
Cited alongside, same era.
Perturbation of matrices and nonnegative rank with a view toward statistical models
C. Bocci, E. Carlini, and F. Rapallo · 2011
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Computing a nonnegative matrix factorization–provably
S. Arora, R. Ge, R. Kannan, and A. Moitra · 2012
Cited alongside, same era.
Approximations of convex bodies by polytopes and by projections of spectrahedra
A. Barvinok · 2012
Cited alongside, same era.
Semidefinite Optimization and Convex Algebraic Geometry
G. Blekherman, P. A. Parrilo, and R. Thomas, editors · 2012
Cited alongside, same era.
J. Gouveia, P.A. Parrilo, and R.R. Thomas · 2013
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Polytopes of minimum positive semidefinite rank
J. Gouveia, R. Z. Robinson, and R. R. Thomas · 2013
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Worst-case results for positive semidefinite rank
J. Gouveia, R. Z. Robinson, and R. R. Thomas · 2013
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Efficient protocols for generating bipartite classical distributions and quantum states
R. Jain, Y. Shi, Z. Wei, and S. Zhang · 2013
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M. Laurent and T. Piovesan · 2013
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An almost optimal algorithm for computing nonnegative rank
A. Moitra · 2013
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Rational and real positive semidefinite rank can be different
J. Gouveia, H. Fawzi, and R. Z. Robinson · 2014
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Smallest compact formulation for the permutahedron
M. Goemans · 2014
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Some upper and lower bounds on psd rank
T. Lee, Z. Wei, and R. de Wolf · 2014
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