LASSO uses an $L_1$ penalty and can encounter two important limitations: when the number of predictors exceeds the number of examples, it selects at most as many predictors as there are examples before saturating; and among highly correlated predictors, it tends to select one while excluding the others. Elastic net combines the LASSO penalty with a quadratic $L_2$ penalty, helping address these limitations. When its $L_2$ component is positive, the objective is strongly convex and has a unique minimum. LASSO and ridge regression are special cases of elastic net. A naive elastic-net procedure first estimates ridge coefficients for a fixed $\lambda_2$ and then applies LASSO-type shrinkage, causing double shrinkage that can increase bias and impair prediction. Rescaling the resulting coefficients by $1+\lambda_2$ corrects this additional shrinkage.