Inertial Bregman Proximal Gradient Algorithm For Nonconvex Problem with Smooth Adaptable Property

In this paper we study the problems of minimizing the sum of two nonconvex functions: one is differentiable and satisfies smooth adaptable property. The smooth adaptable property, also named relatively smooth condition, is weaker than the globally gradient Lipschitz continuity. We analyze an inertial version of the Bregman Proximal Gradient (BPG) algorithm and prove its stationary convergence. Besides, we prove a sublinear convergence of the inertial algorithm. Moreover, if the objective function satisfies Kurdyka--{\L}ojasiewicz (KL) property, its global convergence to a critical point of the objective function can be also guaranteed.