  The Alternating Direction Method of Multipliers (ADMM) has now days gained
tremendous attentions for solving large-scale machine learning and signal
processing problems due to the relative simplicity. However, the two-block
structure of the classical ADMM still limits the size of the real problems
being solved. When one forces a more-than-two-block structure by
variable-splitting, the convergence speed slows down greatly as observed in
practice. Recently, a randomly assembled cyclic multi-block ADMM (RAC-MBADMM)
was developed by the authors for solving general convex and nonconvex quadratic
optimization problems where the number of blocks can go greater than two so
that each sub-problem has a smaller size and can be solved much more
efficiently. In this paper, we apply this method to solving few selected
machine learning problems related to convex quadratic optimization, such as
Linear Regression, LASSO, Elastic-Net, and SVM. We prove that the algorithm
would converge in expectation linearly under the standard statistical data
assumptions. We use our general-purpose solver to conduct multiple numerical
tests, solving both synthetic and large-scale bench-mark problems. Our results
show that RAC-MBADMM could significantly outperform, in both solution time and
quality, other optimization algorithms/codes for solving these machine learning
problems, and match up the performance of the best tailored methods such as
Glmnet or LIBSVM. In certain problem regions RAC-MBADMM even achieves a
superior performance than that of the tailored methods.

Optimization and Control;Machine Learning;Machine Learning