Abstract. We propose a new iterative algorithm to solve the variational inequality problem with monotone and Lipschitz continuous mapping in Hilbert space. It is based on two well-known methods: Popov’s 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 feasible set at one iteration. We prove the weak convergence of the sequences generated by the proposed algorithm.
Keywords: variational inequality, monotone mapping, extragradient method, convergence.
Малицкий Юрий Валериевич, аспирант Киевского национального университета имени Тараса Шевченко,
e-mail: y.malitsky@gmail.com.
Семенов Владимир Викторович, доктор физ.-мат. наук, доцент, профессор Киевского национального университета имени Тараса Шевченко,
e-mail: semenov.volodya@gmail.com.