The authors provide a gradient method for the (constrained) multiple-set split convex feasibility problem, finding a point
Here, and are closed convex subsets of the Hilbert spaces and , respectively, and are bounded linear operators. The method bases on the minimization of the function
with suitable positive parameters and (where denotes the projection operator).
It is shown that the iteration sequence generated by the method converges weakly to a solution of the problem. Assuming additional properties for the sets and , even strong convergence can be proved.