A two-step extragradient method for variational inequalities

Finite number of iterations in the two-step extragradient method

“…Recurrent correlations for the two-step extragradient method of solution to variational inequality (1) are the following [8]:…”

“…A new class of extragradient methods is two-step extragradient methods [7,8]. We note that two-step and even three-step methods are not new and are investigated by many scientists [9][10][11], although such methods have obtained their name in view of using several previous iteration points on each iteration, but not due to the use of predictive points, as in [7,8].…”

“…We note that two-step and even three-step methods are not new and are investigated by many scientists [9][10][11], although such methods have obtained their name in view of using several previous iteration points on each iteration, but not due to the use of predictive points, as in [7,8]. The use of earlier obtained iteration points is applied for the regularization and the solution to problems with inexact initial data.…”

“…The use of earlier obtained iteration points is applied for the regularization and the solution to problems with inexact initial data. In paper [12] one expresses the idea of multi-step methods, which are structurally similar to the two-step extragradient method [7,8]. At the same time, in [12] one investigates methods with the one-step extrapolation, which is applied for the construction of strictly separating hyper-plane, with different modes for the choice of the main and extrapolating step.…”

Multi-Step Algorithms for Solving Equilibrium Problems

“…Due to this reason, the extragradient method has recieved a lot of attention by many authors who have modified it via many ways, for instance [5,15] and the references therein. Recently, Zykina and Melenchuk [27] have introduced a two-step extragradient method with a suitable fixed stepsize β > 0 for VIPs in Euclidean spaces. In this method, three projections on feasible set needed to be computed per each iteration.…”