Boundedness and convergence of online gradient method with penalty and momentum

In this paper, the deterministic convergence of an online gradient method with penalty and momentum is investigated for training two-layer feedforward neural networks. The monotonicity of the new error function with the penalty term in the training iteration is firstly proved. Under this conclusion, we show that the weights are uniformly bounded during the training process and the algorithm is deterministically convergent. Sufficient conditions are also provided for both weak and strong convergence results.