A strong convergence theorem for an iterative method for solving the split variational inequalities in Hilbert spaces (Q2054675)

In this paper, a strong convergence theorem is given for the iteration of an algorithm to solve certain variational inequalities. The hypotheses are mild. These problems are called split variational inequalities. Not only the strong convergence result, but also the iterative method are new. The authors view this task as an optimization problem. The problem is a particularly difficult one, because one wishes to find a solution that satisfies certain inequalities which must be in a provided convex set and whose image by a linear operator is also in (another) given convex set, both at the same time. The operator is supposed to be bounded in order to make the mathematical problem feasible. The authors' algorithm is a modification of the well-known CQ algorithm which is essentially a projection gradient pursuit method.