Alternating Direction Method of Multipliers for Nonparallel Support Vector Machines

Recently, a novel nonparallel support vector machine(NPSVM) is proposed by Tian et al, which has several attracting advantages over its predecessors. A sequential minimal optimization algorithm(SMO) has already been provided to solve the dual form of NPSVM. Different from the existing work, we present a new strategy to solve the primal form of NPSVM in this paper. Our algorithm is designed in the framework of the alternating direction method of multipliers(ADMM), which is well suited to distributed convex optimization. Although the closed-form solution of each step can be written out directly, in order to be able to handle problems with a very large number of features or training examples, we propose to solve the underlying linear equation systems proximally by the conjugate gradient method. Experiments are carried out on several data sets. Numerical results indeed demonstrate the effectiveness of our method.