A generalized Douglas-Rachford splitting algorithm for nonconvex optimization

In this paper, we propose a generalized Douglas-Rachford splitting method for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the generalized Douglas-Rachford splitting method. We then apply the generalized Douglas-Rachford splitting method to two important classes of nonconvex optimization problems arising in data science: low rank matrix completion and logistic regression. Numerical results validate the effectiveness of our generalized Douglas-Rachford splitting method compared with some other classical methods.