Extensions of S-Lemma for Noncommutative Polynomials
Optimization and Control
2022-07-06 v2 Operator Algebras
Abstract
We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is positive semidefinite if and only if its coefficient matrix is positive semidefinite. Then we extend the S-lemma to three kinds of noncommutative polynomials: noncommutative polynomials whose coefficients are real numbers, matrix-valued noncommutative polynomials and hereditary polynomials.
Cite
@article{arxiv.2207.00840,
title = {Extensions of S-Lemma for Noncommutative Polynomials},
author = {Feng Guo and Sizhuo Yan and Lihong Zhi},
journal= {arXiv preprint arXiv:2207.00840},
year = {2022}
}