An extended Newton-type algorithm for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2442" altimg="si3.svg"><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-regularized sparse logistic regression and its efficiency for classifying large-scale datasets

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version to sparsity constrained models. This paper is carried out on regression by Newton method. We begin with establishing first-order optimality condition associated a $\tau$-stationary point. point can be equivalently interpreted system equations which then efficiently solved The method considerably low computational complexity and enjoys global quadratic convergence properties. Numerical experiments random real data demonstrate superior performance when against seven state-of-the-art solvers.