The improved inertial S-subgradient projection algorithm for non-convex split feasibility problems

Split feasibility problem is a kind of very important common mathematical problem, which is applied in many fields such as signal processing, image restoration, and intensity modulated radiation therapy. With the development of society and the needs of production practice, the application of split feasibility problem in various fields is no longer limited to convex sets. However, there is still relatively a little research on non-convex situations, and the algorithms related to subgradient projection for solving non-convex split feasibility problem lack the validation of numerical experiments. In this paper, we explore non-convex split feasibility problem and propose an improved inertial S-subgradient projection algorithm. We prove the weak convergence of the algorithm and provide step length conditions independent of the matrix spectral radius. At the same time, we verify the feasibility and effectiveness of the algorithms through numerical experiments.