The Extragradient Method And Its Modification For Variational Inequality

This paper presents the extragradient method and its modification for variational inequality problem. In Chapter two, we extend the modified extragradient method which is proposed by Wang, Xiu and Zhang[1] to infinite-dimensional Hilbert space, and discuss convergence of a modified extragradient method for pseudomonotone variational inequality in infinite-dimensional Hilbert space. In Chapter three, we modify extragradient method with different Armijo-type linesearch and profitable direction from paper [1] in the finite-dimensional space, then we use numerical experiments to compare our method with algorithm [1] to see its advantages. In Chapter four, we improve the projection algorithm proposed by Yan, Han and Sun[2].