A NEW INERTIAL SELF-ADAPTIVE ALGORITHM FOR SPLIT COMMON FIXED-POINT PROBLEMS

In this paper, we study the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space. We establish a weak convergence theorem of the proposed iterative algorithm, which combines the primal-dual method and the inertial method. In our algorithm, the step sizes are chosen self-adaptively so that the implementation of the algorithm does not need any prior information about bounded linear operator norms. Finally, numerical results are included to illustrate the efficiency of the proposed algorithm.

Automated summary

This paper studies the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space and establishes a weak convergence theorem for the proposed iterative algorithm, which combines the primal-dual method and the inertial method. The algorithm adapts step sizes self-adaptively, eliminating the need for prior information about bounded linear operator norms. Numerical results demonstrate the efficiency of the proposed algorithm.