A parameterized Douglas–Rachford splitting algorithm for nonconvex optimization

In this paper, we study a parameterized Douglas–Rachford splitting method in Wang-Wang (2019)[5] 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. As a by-product, this also provides convergence results of a special case of the adaptive Douglas–Rachford algorithm proposed by Dao and Phan (2019)[22] in nonconvex settings. 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.