A hybrid projection method for solving the multiple-sets split feasibility problem

This paper studies the multiple-sets split feasibility problem in Hilbert spaces. To solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Our scheme combines the hybrid projection method with the proximal point algorithm. We show that the iterative method converges strongly under weaker assumptions than the ones used recently by Yao et al. (Optimization 69(2):269-281, 2020). We also study an application to the split feasibility problem and give a strong convergence result to the minimum-norm solution to the problem. Thereafter, some numerical examples are conducted in order to illustrate the convergence analysis of the considered methods as well as compare our results to the related ones introduced by Buong (Numer Algorithms 76:783-798, 2017) and Yao et al. (2020). We end this paper by considering an application of our method to a class of optimal control problems and compare our result with the one introduced by Anh et al. (Acta Math Vietnam 42:413-429, 2017).