On global optimizations with polynomials

We consider the problem of finding the (unconstrained) global minimum of a real valued polynomial . We study the problem of finding the bounds of global minimizers. It is shown that the unconstrained optimization reduces to some constrained optimizations which can be approximated by solving some convex linear matrix inequality (LMI) problems. This research was partly supported by the National Science Foundation of China under grant No. 10671145.