Alternating Iterative Algorithms for the Split Equality Problem Without Prior Knowledge of Operator Norms

In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several modified algorithms in which the selection of the stepsize is independent of the norms. In particular, we consider the case whenever the convex sets involved are level sets of given convex functions.