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An approximate proximal-extragradient type method for monotone variational inequalities. (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.

65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
49M20Methods of relaxation type in calculus of variations