Konnov, I. V. 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. Cited in 15 Documents MSC: 90C30 Nonlinear programming 91A05 2-person games 90C26 Nonconvex programming, global optimization 90-08 Computational methods for problems pertaining to operations research and mathematical programming Keywords:saddle points; equilibrium points; variational inequalities PDFBibTeX XMLCite \textit{I. V. Konnov}, Russ. Math. 37, No. 12, 89--92 (1993; Zbl 0842.90108); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 12, 89--92 (1993)