Semidefinite Descriptions of the Convex Hull of Rotation Matrices
| Autor: | James Saunderson, Pablo A. Parrilo, Alan S. Willsky |
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| Rok vydání: | 2015 |
| Předmět: |
Convex hull
Semidefinite programming Mathematics::Optimization and Control Regular polygon Rotation matrix Positive-definite matrix Theoretical Computer Science Combinatorics Optimization and Control (math.OC) FOS: Mathematics Affine space 90C22 90C25 52A41 52A20 Orthogonal group Orthogonal matrix Mathematics - Optimization and Control Software Mathematics |
| Zdroj: | SIAM Journal on Optimization. 25:1314-1343 |
| ISSN: | 1095-7189 1052-6234 |
| Popis: | 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. 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. 29 pages, 1 figure |
| Databáze: | OpenAIRE |
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