We investigate and demonstrate the benefits of applying interior point methods (IPM) in supervised learning of artificial neural networks. Specifically, three IPM algorithms are presented in this paper: a deterministic logarithmic barrier (LB), a stochastic logarithmic barrier function (SB) and a quadratic trust region method respectively. Those are applied to the training of supervised feedforward artificial neural networks. We consider neural network training as a nonlinear constrained optimization problem. Specifically, we put constraints on the weights to avoid network paralysis. In the case of the (LB) method, the search direction is derived using a recursive prediction error method (RPEM) that approximates the inverse of the Hessian of a logarithmic error function iteratively. The weights move on a center trajectory in the interior of the feasible weight space and have good convergence properties. For its stochastic version, at each iteration a stochastic optimization procedure is used to add random fluctuations to the RPEM direction in order to escape local minima. This optimization technique can be viewed as a hybrid of the barrier function method and simulated annealing procedure. In the third algorithm, we approximate the objective function by a quadratic convex function and use a trust region method to find the optimal weights. Computational experiments in approximation of discrete dynamical systems and medical diagnosis problems are also provided.