Global polynomial optimization via Groebner basas

Finding the global optimal solution for a general nonlinear optimization problems is a difficult task except for very small problems. In this paper we identify a class of nonlinear optimization problems called polynomial optimization problems(PO). A polynomial optimization is an optimization problem with a scalar polynomial objective function and a set of polynomial constraints. we employ the technique of Groebner basis (GB) as a useful method for finding optimal solutions in PO problems.To apply GB theory,we need to consider the Lagrangian problem associated with the original PO and extract the system of nonlinear equations associated with the first-order Karush-Kuhn-Tucker (KKT). By using Groebner Bases, we can determine the global minimum of a polynomial program in a reasonable amount of time and memory.