Gradient Descent for Elastic net Regression

I am using the from the wikipedia page to find the gradient descent. https://en.wikipedia.org/wiki/Elastic_net_regularization.

What will be gradient descent equation for this. ?

And as for ridge regression if i am using very large data sets. Instead of calculating the inverse is there another way to calculate it.

Ridge Regression eqn - ˆθ = (X^T. X + λI)^−1.X^T .y

Thanks