Improved approximation results on standard quartic polynomial optimization

In this paper, we consider the problem of approximately solving standard quartic polynomial optimization (SQPO). Using its reformulation as a copositive tensor programming, we show how to approximate the optimal solution of SQPO by using a series of polyhedral cones to approximate the cone of copositive tensors. The established quality of approximation is sharper than the ones studied in the literature. As an interesting extension, we also propose some approximation bounds on multi-homogenous polynomial optimization problems.