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We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of Sum-of-Squares (SOS) relaxations.
Certain integrals and infinite series involving ultra-spherical polynomials and Bessel functions
H.-y. Hsu · 1938
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On the field of values of a matrix
L. Brickman · 1961
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Remarks on the extreme eigenvalues of Toeplitz forms associated with orthogonal polynomials
S. V. Parter · 1965
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Extreme eigenvalues of Toeplitz matrices associated with certain orthogonal polynomials
J. V. Baxley · 1971
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Positive maps of low dimensional matrix algebras
S. L. Woronowicz · 1976
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Uniform denominators in Hilbert’s seventeenth problem
B. Reznick · 1995
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Separability and distillability in composite quantum systems-a primer
M. Lewenstein, D. Bruß, J. I. Cirac, B. Kraus, M. Kuś, J. Samsonowicz, A. Sanpera, and &. R. Tarrach · 2000
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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
P. A. Parrilo · 2000
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Mixed-state entanglement and quantum communication
M. Horodecki, P. Horodecki, and R. Horodecki · 2001
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Global optimization with polynomials and the problem of moments
J. B. Lasserre · 2001
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Distinguishing separable and entangled states
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri · 2002
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Classical deterministic complexity of Edmonds’ problem and quantum entanglement
L. Gurvits · 2003
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Random walk in a simplex and quadratic optimization over convex polytopes
Y. Nesterov · 2003
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Zeros of Gegenbauer and Hermite polynomials and connection coefficients
I. Area, D. Dimitrov, E. Godoy, and A. Ronveaux · 2004
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Convexity properties of the cone of nonnegative polynomials
G. Blekherman · 2004
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Complete family of separability criteria
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri · 2004
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On the equivalence of algebraic approaches to the minimization of forms on the simplex
E. de Klerk, M. Laurent, and P. Parrilo · 2005
Cited alongside, same era.
A most compendious and facile quantum de Finetti theorem
R. Koenig and G. Mitchison · 2009
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The power of symmetric extensions for entanglement detection
M. Navascues, M. Owari, and M. B. Plenio · 2009
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Hypercontractivity, sum-of-squares proofs, and their applications
B. Barak, F. G. Brandao, A. W. Harrow, J. Kelner, D. Steurer, and Y. Zhou · 2012
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Bounds for extreme zeros of some classical orthogonal polynomials
K. Driver and K. Jordaan · 2012
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Convergence of SDP hierarchies for polynomial optimization on the hypersphere
A. C. Doherty and S. Wehner · 2012
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Approximation quality of SOS relaxations, 2013
P. A. Parrilo · 2013
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One-and-a-half quantum de Finetti theorems
M. Christandl, R. König, G. Mitchison, and R. Renner · 2007
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A survey of the s-lemma
I. Pólik and T. Terlaky · 2007
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The complexity of optimizing over a simplex, hypercube or sphere: a short survey
E. De Klerk · 2008
Cited alongside, same era.
Polynomial optimization on odd-dimensional spheres
J. P. D’Angelo and M. Putinar · 2009
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Weak decoupling, polynomial folds and approximate optimization over the sphere
V. Bhattiprolu, M. Ghosh, V. Guruswami, E. Lee, and M. Tulsiani · 2017
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Quantum entanglement, sum of squares, and the log rank conjecture
B. Barak, P. K. Kothari, and D. Steurer · 2017
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E. de Klerk and M. Laurent · 2019
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http://dlmf.nist.gov/, Release 1.0.22 of 2019-03-15
NIST Digital Library of Mathematical Functions · 2019
Closest in time.