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