  This paper presents a regularized Newton method (RNM) with generalized
regularization terms for unconstrained convex optimization problems. The
generalized regularization includes quadratic, cubic, and elastic net
regularizations as special cases. Therefore, the proposed method serves as a
general framework that includes not only the classical and cubic RNMs but also
a novel RNM with elastic net regularization. We show that the proposed RNM has
the global $\mathcal{O}(k^{-2})$ and local superlinear convergence, which are
the same as those of the cubic RNM.
