LASSO

LASSO stands for Least Absolute Shrinkage and Selection Operator. It is the combination of MSE and L1 norm.

$$w_{\text{lasso}}=\underset{w}{\mathrm{argmin}}\Vert y-Xw{\Vert }^2+\lambda \Vert w{\Vert }_1.$$

The L1 Regularization not only penalizes the overfitting, but also encourages sparsity (refer to Sparsity).

LASSO can be efficiently solved by methods such as projected GD, PGM, and ADMM.