| 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]. |
