Which Symmetric Homogeneous Polynomials Can Be Proved Positive Semi-definite by Difference Substitution Method?

摘要

Recently a method based on substitution of difference of variables has been developed by Yang [12] for verifying the positive semi-definiteness of homogeneous polynomials. In this paper, we investigate the structure of the cone formed by all symmetric homogeneous polynomials whose positive semi-definiteness can proven by difference substitution method.