Relaxed two points projection method for solving the multiple-sets split equality problem
Let \(H_1\), \(H_2\), \(H_3\) be real Hilbert spaces, \(C_i \subset H_1\), \(i=1,\dots,t\), \(Q_j \subset H_2\), \(j=1,\dots,r\) be closed convex sets, and \(A\in L(H_1, H_2)\), \(B\in L(H_2,H_3)\). The authors consider the problem of finding a point \(x\) such that \(x\in \cap_{i=1}^t C_i\), \(y\in \cap_{j=1}^r Q_j\) and \(Ax=By\). First, the original problem is transferred to an optimization problem. Next, the authors present a modified gradient projection algorithm to solve the problem and under suitable conditions establish the weak convergence of approximations to the solution. Numerical experiments are also discussed.
scientific article; zbMATH DE number 6871988
scientific article