Semidefinite Descriptions of the Convex Hull of Rotation Matrices
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 s...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Society for Industrial and Applied Mathematics
2016
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| Online Access: | http://hdl.handle.net/1721.1/100895 https://orcid.org/0000-0003-1132-8477 https://orcid.org/0000-0003-0149-5888 |
| Summary: | 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. |
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