What is the advantage of using the regularized regression with both L-1 and L-2 penalty term?


New Member
I have currently read an article on predicting gene expression level using genotype data.
The method in this paper used the regularized linear regression as its predictive model.

The point is, it has both L1 and L2 penalty terms in its objective function to be minimized.
I'm aware that Elastic Net, an intermediate model between LASSO and Ridge regression, employs both models' penalty mechanisms to overcome their limitations. And it includes the alpha parameter to control the weights of the contribution of L1 and L2 penalty term.

The model from the paper doesn't have such parameter. It just has L1 and L2 penalty terms having the same lambda parameter which determines the extent of the penalty.

Is there any reason that such form of regularized regression is used ??