The Linear Convergence for Strongly Pseudomonotone Variational Inequalities

Under the assumptions of the strong pseudomonotonicity, the extragradient method for solving the variational inequality is linearly convergent.Since the extragradient method needs to project twice onto the closed convex set, the projection is usually difficult to calculate especially when closed convex set is complex.In order to overcome this shortcoming, one needs modifiy the extragradient method, thus the subgradient extragradient method for solving strongly pseudomonotone variational inequality was proposed.At each iteration, only one projection needs to be executed onto the closed convex set.The research has shown that iterative sequences generated by the subgradient extragradient method for solving the strongly pseudomonotone variational inequality is linearly convergent.By using of the subgradient extragradient method for solving the strongly pseudomonotone variational inequality, the convergence of iterative sequences is accelerated to some extent.