A Smoothing Algorithm for l1 Support Vector Machines. (arXiv:2401.09431v1 [math.OC])

A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important measure of its cost for very large datasets. The algorithm uses smoothing for the hinge-loss function, and an active set approach for the $\ell^{1}$ penalty. The smoothing parameter $\alpha$ is initially large, but typically halved when the smoothed problem is solved to sufficient accuracy. Convergence theory is presented that shows $\mathcal{O}(1+\log(1+\log_+(1/\alpha)))$ guarded Newton steps for each value of $\alpha$ except for asymptotic bands

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