A Double Projection Algorithm For Solving Variational Inequality Problems

The projection algorithm is an effective method for solving variational inequality problems.The original projection algorithm computes the projection once during each iteration,but requires that the mapping involved in the variational inequality problems be strongly monotone and Lipschitz continuous.The double projection algorithm adds a projection onto a hyperplane during each iteration,which has the advantage of weakening the monotonicity requirement of the mapping.This thesis reviews the development process from the original projection algorithm to the latest double projection algorithm for solving variational inequality problems.A new double projection algorithm for solving variational inequality problems is proposed by selecting a new hyperplane.Under the condition that the solution set of the dual variational inequality problems is not empty,the global convergence of the new algorithm is proved.Numerical experiment results are also reported.