# Adding regularization term to perceptron weight update

I hope this isn't a stupid question. I'm trying to reduce overfitting on my perceptron network by adding in a regularization term. However I am not sure where the actual term goes...

Usually the regularization term is shown in the literature as being added to the cost function, like so:

$$J(w) = \sum_{i=1}^n (y^i - ypr^i)^2 + \lambda\sum_{j = 1}^m|w_j|$$

However I don't know how exactly this applies to the weight update equation for the perceptron:

$$w = w_j(t) + n(y^i - ypr^i)x$$

Do I put the regularization term within the brackets (above) and therefore multiply it by the learning rate and the data?...