Polyak's gradient method for split feasibility problem constrained by level sets

In this paper, we are concerned with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying Polyak's gradient method, we get a new and simple algorithm for such a problem. Under standard assumptions, we prove that the whole sequence generated by the algorithm weakly converges to a solution. We also modify the proposed algorithm and state the strong convergence without regularity conditions on the sets involved. Numerical experiments are included to illustrate its applications in signal processing.