On semi-definiteness and minimal H-eigenvalue of a symmetric space tensor using nonnegative polynomial optimization techniques

作者：

Highlights：

• We find two methods to verify the positive semi-definiteness of a symmetric space tensor.

• The first method could verify the positive semi-definiteness of a symmetric space tensor in polynomial time.

• The second method could verify the positive semi-definiteness of a symmetric space tensor in the large order case.

• We discuss the method how to solve the H-eigenvalue of a symmetric space tensor.

摘要

•We find two methods to verify the positive semi-definiteness of a symmetric space tensor.•The first method could verify the positive semi-definiteness of a symmetric space tensor in polynomial time.•The second method could verify the positive semi-definiteness of a symmetric space tensor in the large order case.•We discuss the method how to solve the H-eigenvalue of a symmetric space tensor.

论文关键词：Space tensor,Nonnegative polynomials,Semidefinite program,H-eigenvalue

论文评审过程：Received 23 November 2017, Revised 23 May 2018, Accepted 6 July 2018, Available online 10 July 2018, Version of Record 12 March 2019.

论文官网地址：https://doi.org/10.1016/j.image.2018.07.006