A generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regression

A large family of paradigmatic models arising in the area of image/signal processing, machine learning and statistics regression can be boiled down to consensus optimization. This paper is devoted to a class of consensus optimization by reformulating it as monotone plus skew-symmetric inclusion. We propose a distributed optimization method by deploying the algorithmic framework of generalized alternating direction implicit method. Under some mild conditions, the proposed method converges globally. Furthermore, the preconditioner is exploited to expedite the efficiency of the proposed method. Numerical simulations on sparse logistic regression are implemented by variant distributed fashions. Compared to some state-of-the-art methods, the proposed method exhibits appealing numerical performances, especially when the relaxation factor approaches to zero.