We consider here the problem of minimizing a polynomial function on $\oR^n$. The problem is known to be hard even for degree $4$. Therefore approximation algorithms are of interest. Lasserre \cite{lasserre:2001} and Parrilo \cite{Pa02a} have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose here a method for computing a converging sequence of upper bounds using semidefinite programming based on perturbing the original polynomial. The method is applied to several examples.

## Citation

To appear in SIAM Journal on Optimization

## Article

View Semidefinite Approximations for Global Unconstrained Polynomial Optimization