An Extragradient Algorithm for Monotone Variational Inequalities

A new iterative algorithm is proposed for solving the variational inequality problem with a monotone and Lipschitz continuous mapping in a Hilbert space. The algorithm is based on the following two well-known methods: the Popov algorithm and so-called subgradient extragradient algorithm. An advantage of the algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration. The weak convergence of sequences generated by the proposed algorithm is proved.