# Is decision boundary of penalized logistic regression linear?

The decision boundary of SVM is a straight line. If we use e.g. RBF kernel, decision boundary is linear in hilbert space, but it the original space it is non-linear. I assume that the logistic regression has linear decision boundary. Is it linear also after using of penalty term, such as elastic net?

• @strateeg32 I said logistic regression classifier in my post, not logistic regression. It's used with a threshold which boils down to a classifier in the form $w^Tx+b>\tau$, a hyper-plane. Mar 7 '20 at 23:52