  Support vector machines (SVMs) with sparsity-inducing nonconvex penalties
have received considerable attentions for the characteristics of automatic
classification and variable selection. However, it is quite challenging to
solve the nonconvex penalized SVMs due to their nondifferentiability,
nonsmoothness and nonconvexity. In this paper, we propose an efficient
ADMM-based algorithm to the nonconvex penalized SVMs. The proposed algorithm
covers a large class of commonly used nonconvex regularization terms including
the smooth clipped absolute deviation (SCAD) penalty, minimax concave penalty
(MCP), log-sum penalty (LSP) and capped-$\ell_1$ penalty. The computational
complexity analysis shows that the proposed algorithm enjoys low computational
cost. Moreover, the convergence of the proposed algorithm is guaranteed.
Extensive experimental evaluations on five benchmark datasets demonstrate the
superior performance of the proposed algorithm to other three state-of-the-art
approaches.
