Matrix Cubes Parametrized by Eigenvalues
Optimization and Control
2008-04-29 v1 Algebraic Geometry
Abstract
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric matrices. An LMI representation is given for the convex set of all feasible instances, and its boundary is studied from the perspective of algebraic geometry. This generalizes the earlier work [12] with Parrilo on k-ellipses and k-ellipsoids.
Cite
@article{arxiv.0804.4462,
title = {Matrix Cubes Parametrized by Eigenvalues},
author = {Jiawang Nie and Bernd Sturmfels},
journal= {arXiv preprint arXiv:0804.4462},
year = {2008}
}
Comments
12 pages, 1 figure