Semidefinite Descriptions of the Convex Hull of Rotation Matrices
Author(s)Saunderson, James; Parrilo, Pablo A.; Willsky, Alan S.
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We study the convex hull of SO(n), the set of n x n orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of SO(n) is doubly spectrahedral, i.e., both it and its polar have a description as the intersection of a cone of positive semidefinite matrices with an affine subspace. Our spectrahedral representations are explicit and are of minimum size, in the sense that there are no smaller spectrahedral representations of these convex bodies.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
SIAM Journal on Optimization
Society for Industrial and Applied Mathematics
Saunderson, J., P. A. Parrilo, and A. S. Willsky. “Semidefinite Descriptions of the Convex Hull of Rotation Matrices.” SIAM Journal on Optimization 25, no. 3 (January 2015): 1314–1343.
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