A Neural Network is trained to forecast a moving trajectory. The neural network training is formulated as a nonlinear programming problem and a Newton method is used to find the optimal weights. The learning Algorithm is derived using a Recursive Prediction Error Method that approximates the inverse of the Hessian. Furthermore, box Constraints are added to the network weights to avoid network paralysis and a constraint nonlinear programming problem is formulated. Logarithmic Barrier methods which are a class of Interior Point Methods are presented. Interior point methods have good convergence properties because the weights move on a center path in the interior of the feasible weight. The logarithmic barrier method is combined with the Newton method to form a Newton-Barrier method. The moving missile trajectory is simulated using differential equations and the proposed algorithm is used to train the network in order to forecast the missile position at any given time.