Splitting of the gradient approach for solving extreme inclusions (Q1571195)

The author considers the problem of calculating a fixed point of an extreme mapping. A new approach is proposed in which the solution of the original equilibrium problem reduces to the combined solution of an optimization problem and a saddle-point problem. The convergence of the prediction-type gradient method to a stationary point is proved in the nonconvex case, and the monotonic convergence is established in the convex case.