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In this paper we study the problems of minimizing the sum of two nonconvexfunctions: one is differentiable and satisfies smooth adaptable property. Thesmooth adaptable property, also named relatively smooth condition, is weakerthan the globally gradient Lipschitz continuity. We analyze an inertial versionof the Bregman Proximal Gradient (BPG) algorithm and prove its stationaryconvergence. Besides, we prove a sublinear convergence of the inertialalgorithm. Moreover, if the objective function satisfiesKurdyka--{\L}ojasiewicz (KL) property, its global convergence to a criticalpoint of the objective function can be also guaranteed.

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