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?
The penalty terms are regularisation terms that affect the training process and thus the decision boundary found (i.e. weights and/or bias). Once trained, the prediction is not affected by neither the regularisation method nor the loss function. So, any linear classifier/regressor is still linear after penalisation. That said, since logistic regression classifier has a linear decision boundary, it'll still have a linear decision boundary when penalised.