  The l1-regularized logistic regression is a widely used statistical model in
data classification. This paper proposes a dual Newton method based proximal
point algorithm (PPDNA) to solve the l1-regularized logistic regression problem
with bias term. The global and local convergence of PPDNA hold under mild
conditions. The computational cost of a semismooth Newton (Ssn) algoithm for
solving subproblems in the PPDNA can be effectively reduced by fully exploiting
the second-order sparsity of the problem. We also design an adaptive sieving
(AS) strategy to generate solution paths for the l1-regularized logistic
regression problem, where each subproblem in the AS strategy is solved by the
PPDNA. This strategy exploits active set constraints to reduce the number of
variables in the problem, thereby speeding up the PPDNA for solving a series of
problems. Numerical experiments demonstrate the superior performance of the
PPDNA in comparison with some state-of-the-art second-order algorithms and the
efficiency of the AS strategy combined with the PPDNA for generating solution
paths.
