An inertial Douglas-Rachford splitting algorithm for nonconvex and nonsmooth problems

In the fields of wireless communication and data processing, there are varieties of mathematical optimization problems, especially nonconvex and nonsmooth problems. For these problems, one of the biggest difficulties is how to improve the speed of solution. To this end, here we mainly focused on a minimization optimization model that is nonconvex and nonsmooth. Firstly, an inertial Douglas-Rachford splitting (IDRS) algorithm was established, which incorporate the inertial technology into the framework of the Douglas-Rachford splitting algorithm. Then, we illustrated the iteration sequence generated by the proposed IDRS algorithm converges to a stationary point of the nonconvex nonsmooth optimization problem with the aid of the Kurdyka-Lojasiewicz property. Finally, a series of numerical experiments were carried out to prove the effectiveness of our proposed algorithm from the perspective of signal recovery. The results are implicit that the proposed IDRS algorithm outperforms another algorithm.