SELF-ADAPTIVE STEPSIZE METHOD WITH INERTIAL EFFECTS FOR SOLVING GENERALIZED SPLIT FEASIBILITY PROBLEMS WITH APPLICATIONS

In this paper, we consider a class of generalized split feasibility problem over the solution set of monotone variational inclusion problems, which includes the split common null point problem, the split variational problems, and other related split type problems. We propose a new self-adaptive stepsize method coupled with inertial extrapolation techniques for solving this problem in real Hilbert spaces. We prove that the sequence generated by the proposed method converges strongly to a solution of the problem under the assumption that the associated singlevalued operator in the monotone variational inclusion problem is not required to be inverse-strongly monotone. Our method uses the stepsizes that are generated at each iteration by some simple calculations, which allows it to be easily implemented without the prior knowledge of the operator norm or the Lipschitz constant of the singlevalued operator. Finally, we apply our results to solve optimal control problems, split linear inverse problems, and least absolute selection and shrinkage operator problems.