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We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming.
Doubly stochastic matrices and the diagonal of a rotation matrix
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The theory of homogeneous convex cones
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R. Sanyal, F. Sottile, and B. Sturmfels · 2011
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Efficient rounding for the noncommutative Grothendieck inequality, 2012
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Semidefinite optimization and convex algebraic geometry
G. Blekherman, P. A. Parrilo, and R. R. Thomas, editors · 2013
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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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Equivariant semidefinite lifts and sum-of-squares hierarchies, 2013
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Lifts of convex sets and cone factorizations
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Worst-case results for positive semidefinite rank, 2013
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Algebraic boundaries of SO ( 2 ) \mathrm{SO}(2) -orbitopes
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