  The canonical duality theory has provided with a unified analytic solution to
a range of discrete and continuous problems in global optimization, which can
transform a nonconvex primal problem to a concave maximization dual problem
over a convex domain without duality gap. This paper shows that under certain
conditions, this canonical dual problem is equivalent to the standard
semi-definite programming (SDP) problem, which can be solved by well-developed
software packages. In order to avoid certain difficulties of using the SDP
method, four strategies are proposed based on unconstrained approaches, which
can be used to develop algorithms for solving some challenging problems.
Applications are illustrated by fourth-order polynomials benchmark optimization
problems.
