In nonlinear model predictive control algorithms, a nonlinear objective function is minimized on-line at every sampling time. Finding a global optimum is not very easy as the objective function is generally nonlinear and nonconvex. In this paper we show that the structure of the polynomial ARX models lends model predictive algorithms some useful properties that are helpful in determining the global optimum solution. The approach used is based on transformation and change of variables to recast the problem into a convex objective function with convex constraints. A method is then proposed that guarantees a global solution to the optimization problem.