New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem

Abstract In this paper, we propose two hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem. Based on algorithm, firstly add term into iteration to accelerate convergence of and adopt flexible rules selecting stepsize shrinking region, which makes an optimal available at each iteration. The region is intersection three sets, are set C hyperplanes. Furthermore, modify Armijo-type step in presented algorithm get a new algorithm.The shown be convergent under certain mild assumptions. Besides, numerical examples given show that proposed have better performance than general algorithm.