Convergence of gradient method with penalty for Ridge Polynomial neural network

In this paper, a penalty term is added to the conventional error function to improve the generalization of the Ridge Polynomial neural network. In order to choose appropriate learning parameters, we propose a monotonicity theorem and two convergence theorems including a weak convergence and a strong convergence for the synchronous gradient method with penalty for the neural network. The experimental results of the function approximation problem illustrate the above theoretical results are valid.