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This work is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization.
On non-negative forms in real variables some or all of which are non-negative
P. H. Diananda · 1962
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Interior-point polynomial algorithms in convex programming , vol. 13 of SIAM Studies in Applied Mathematics
Y. Nesterov and A. Nemirovski · 1994
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Quadratic maps with convex images
M. Ramana and A. Goldman · 1995
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Some geometric results in semidefinite programming
M. Ramana and A. J. Goldman · 1995
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Semidefinite programming
L. Vandenberghe and S. Boyd · 1996
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Sums of squares of regular functions on real algebraic varieties
——— · 2000
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Handbook of semidefinite programming
H. Wolkowicz, R. Saigal, and L. Vandenberghe (editors) · 2000
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Lectures on modern convex optimization
A. Ben-Tal and A. Nemirovski · 2001
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A representation theorem for certain partially ordered commutative rings
T. Jacobi · 2001
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Positive polynomials
A. Prestel and C. N. Delzell · 2001
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Minimizing polynomial functions
P. A. Parrilo and B. Sturmfels · 2003
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Positivity, sums of squares and the multi-dimensional moment problem. II
S. Kuhlmann, M. Marshall, and N. Schwartz · 2005
Cited alongside, same era.
The Lax conjecture is true
A. S. Lewis, P. A. Parrilo, and M. V. Ramana · 2005
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Linear matrix inequality representation of sets
J. W. Helton and V. Vinnikov · 2007
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Advances in convex optimization: conic programming
A. Nemirovski · 2007
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Positive polynomials and sums of squares , vol. 146 of Mathematical Surveys and Monographs
M. Marshall · 2008
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Semidefinite representation of convex hulls of rational varieties
D. Henrion · 2009
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Theta bodies for polynomial ideals
J. Gouveia, P. A. Parrilo, and R. R. Thomas · 2010
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Obstructions to determinantal representability
P. Brändén
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The matricial relaxation of a linear matrix inequality
J. W. Helton, I. Klep, and S. McCullough
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Semidefinite representation of convex sets
J. W. Helton and J. Nie
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Sufficient and necessary conditions for semidefinite representability of convex sets
———
Cited in the paper.
Convex sets with semidefinite representation
J. B. Lasserre
Cited in the paper.
Exposed faces of semidefinite representable sets
T. Netzer, D. Plaumann, and M. Schweighofer
Cited in the paper.