# optimization – Variant of ridge regression loss function

We can create variants of the loss function, especially of ridge regression by adding more regularizer terms. One of the variants I saw in a book is given below

$$min_{w in mathbf{R}^d} alpha.||w||^2 + (1-alpha).||w||^4 + C||y-X^T.w||^2$$

where $$y in mathbf{R^n}, s in mathbf{R^d}, X in mathbf{R^{dxn}}$$ and $$C$$ a regularization parameter $$in mathbf{R}$$ and $$alpha in (0,1)$$

My question is how does change in $$alpha$$ affects our optimization problem? and how does generally adding more regularizers help? why is not one regularizer enough?