A parameterized Douglas-Rachford Splitting algorithm for nonconvex optimization

Abstract: In this paper, we study a parameterized 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 parameterized Douglas-Rachford splitting method. We then apply the parameterized Douglas-Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas-Rachford splitting method compared with some other classical methods.