Matrix Cubes Parametrized by Eigenvalues

Details Matrix Cubes Parametrized by Eigenvalues Matrix Cubes Parametrized by Eigenvalues

2008-04-28

arxiv.org/abs/0804.4462v1

Mathematics

Optimization and Control

12 pages, 1 figure

Scientific paper

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.

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