A Second-Order Method for Strongly-Convex L1-Regularization Problems


In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed approach is a primal-dual Newton conjugate gradients (pdNCG) method. Convergence properties of pdNCG are studied and worst-case iteration complexity is established. Numerical results are presented on synthetic sparse least-squares problems and real world machine learning problems.

Mathematical Programming, March 2016, Volume 156, Issue 1–2, pp 189–219