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

Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression