  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.

Optimization and Control