Free Semidefinite Representation of Matrix Power Functions
Optimization and Control
2014-10-13 v2
Abstract
Consider the matrix power function X^p defined over the cone of positive definite matrices S^{n}_{++}. It is known that X^p is convex over S^{n}_{++} if p is in [-1,0] or [1,2] and X^p is concave over S^{n}_{++} if p is in [0,1]. We show that the hypograph of X^p admits a free semidefinite representation if p in [0,1] is rational, and the epigraph of X^p admits a free semidefinite representation if p in [-1,0] or [1,2] is rational.
Cite
@article{arxiv.1305.4289,
title = {Free Semidefinite Representation of Matrix Power Functions},
author = {J. William Helton and Jiawang Nie and Jeremy S. Semko},
journal= {arXiv preprint arXiv:1305.4289},
year = {2014}
}
Comments
12 pages, 1 figures