On combined relaxation methods’ convergence rates.

*(English. Russian original)*Zbl 0842.90108
Russ. Math. 37, No. 12, 89-92 (1993); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 12, 89-92 (1993).

Summary: An approach to creating simple and constructive methods for finding saddle points was proposed in a recent paper of the author [Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 10, 30-33 (1992)]. The substantiation of the methods was made there without additional assumptions such as stability of the solution set. Based on this approach methods for finding equilibrium points and solving variational inequalities in the smooth case were proposed in another paper of the author [ibid. 1993, No. 2, 46-53 (1993)]. In the present article we propose a method for the solution of variational inequalities under rather general assumptions, we derive estimates and the convergence rates for the method from the second cited paper above in the unconstrained case.