  In recent years, considerable attention has been devoted to the
regularization models due to the presence of high-dimensional data in
scientific research. Sparse support vector machine (SVM) are useful tools in
high-dimensional data analysis, and they have been widely used in the area of
econometrics. Nevertheless, the non-smoothness of objective functions and
constraints present computational challenges for many existing solvers in the
presence of ultra-high dimensional covariates. In this paper, we design
efficient and parallelizable algorithms for solving sparse SVM problems with
high dimensional data through feature space split. The proposed algorithm is
based on the alternating direction method of multiplier (ADMM). We establish
the rate of convergence of the proposed ADMM method and compare it with
existing solvers in various high and ultra-high dimensional settings. The
compatibility of the proposed algorithm with parallel computing can further
alleviate the storage and scalability limitations of a single machine in
large-scale data processing.
