Strong Convergence of Subgradient Extragradient Methods for the Variational Inequality Problem in Hilbert

We study two projection algorithms for solving the Variational Inequality Problem (VIP) in Hilbert space. One algorithm is a mod-i ed subgradient extragradient method in which an additional pro-jection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.