  The support vector machine (SVM) was originally designed for binary
classifications. A lot of effort has been put to generalize the binary SVM to
multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were
solved by considering their dual formulations which are quadratic programs and
can be solved by standard second-order methods. However, the duals of MSVMs
with regularizers are usually more difficult to formulate and computationally
very expensive to solve. This paper focuses on several regularized MSVMs and
extends the alternating direction method of multiplier (ADMM) to these MSVMs.
Using a splitting technique, all considered MSVMs are written as two-block
convex programs, for which the ADMM has global convergence guarantees.
Numerical experiments on synthetic and real data demonstrate the high
efficiency and accuracy of our algorithms.
