Two-step inertial Bregman alternating structure-adapted proximal gradient descent algorithm for nonconvex and nonsmooth problems

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several iterative algorithms in a way that combines inertial technology and the self-adaptive stepsize such that the implementation of the algorithms doesn’t need any prior information about bounded linear operator norm. Under suitable assumptions, weak convergence of the proposed algorithms is established. As applications, we obtain relative iterative algorithms to solve the multiple-set split feasibility problem. Finally, the performance of the proposed algorithms is illustrated by numerical experiments.