Extragradient methods for pseudomonotone variational inequalities (Q1411517)

One of the most known approaches for constructing projection-based methods converging to a solution of a variational inequality under generalized monotonicity consists in incorporating a predictor step for computing parameters of a separating hyperplane and for providing the the Fejér-monotone convergence. This approach is also known as combined relaxation; see [\textit{I. V.~Konnov}, Russ. Math. 37, No. 2, 44--51 (1993); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 2, 46--53 (1993; Zbl 0835.90123)] and can be extended in several directions; e.g. [\textit{N.Xiu} and \textit{J.~Zhang}, J. Comput. Appl. Math. 152, No.1--2, 559--585 (2003; Zbl 1018.65083)]. The author presents such a method, which uses a modified linesearch procedure and possesses similar convergence properties.