Semidefinite Descriptions of the Convex Hull of Rotation Matrices
Name
Saunderson-2015-Semidefinite descriptions.pdf
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428.09 KB
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Author(s)
Saunderson, James
Parrilo, Pablo A.
Willsky, Alan S.
Date Issued
July 2015
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial and Applied Mathematics
Citation
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.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/14096339x
