*(English)*Zbl 1068.65087

One of the most known approaches to constructing solution methods for monotone variational inequalities consists in incorporating a predictor step for computing parameters of a separating hyperplane and for providing the Fejér-monotone convergence. This approach is also known as combined relaxation; see *I. V. Konnov* [Russ. Mathem. (Iz. VUZ), 37, No. 2, 44–51 (1993; Zbl 0835.90123)] and can be extended in several directions.

*M. V. Solodov* and *B. F. Svaiter* [Math. Progr. 88, 371–389 (2000; Zbl 0963.90064)] proposed an inexact proximal point iteration as the predictor step. The authors suggest a modification of this method which involves an additional projection iteration for completing the predictor step. The method possesses the same convergence properties. Some results of numerical experiments on a network equilibrium problem are reported.

##### MSC:

65K10 | Optimization techniques (numerical methods) |

49J40 | Variational methods including variational inequalities |

49M20 | Methods of relaxation type in calculus of variations |