Hyperplane projection algorithm for split equality problems in Hilbert spaces

The split equality problem has gained significant recognition due to its widespread applicability across various applied mathematical fields. In this present paper, a hyperplane projection algorithm is introduced for solving the split equality problem in Hilbert spaces. This algorithm integrates the hyperplane projection technique with the gradient projection method, utilising Polyak's step sizes for efficient convergence. The weak convergence of our proposed algorithm is demonstrated as well as its relaxed version. Under mild conditions, the strong and linear convergence of the algorithms is established. Numerical experiments conducted on signal recovery problems reveal that our algorithm accelerates the convergence rate and outperforms some existing algorithms.