the feature space appropriately so as to leverage the high accuracy of IPM while maintaining efficiency. Specifically, we propose to solve an elastic-net SVM (ENSVM) or doubly-regularized SVM (DrSVM) [@wang2006doubly] problem during the first phase of the algorithm. The elastic-net regularization performs feature selection with grouping effect and has been shown to be effective on data sets with many but sparse features and high local correlations [@zou2005regularization]. This is the case for text classification, microarray gene expression, and fMRI data sets. The support of the weight vector $w$ for ENSVM usually stabilizes well before the algorithm converges to the optimal solution. Taking advantage of that prospect, we can terminate the first phase of the hybrid algorithm early and proceed to solve a classical SVM problem with the reduced feature set in the second phase, using an IPM solver.

Solving the Elastic Net SVM using ADMM {#sec:admm}
--------------------------------------

SVM can be written in the regularized regression form as $$\label{eq:unconstr_svm}
    \min_{{\textbf{w}},b}\frac{1}{N}\sum_{i=1}^N(1 - (y_i({\textbf{x}_i}^T{\textbf{w}}+ b)))_+ + \frac{\lambda}{2}\|{\textbf{w}}\|_2^2,$$ where the first term is an averaged sum of the hinge losses and the second term is viewed as a ridge regularization on $w$. It is easy to see from this form that the classical SVM 