Double Projection Algorithm For Non-monotonic Variational Inequalities

We propose a double projection algorithm for single-valued variational inequality and set-valued variational inequality in finite-dimensional spaces.Firstly,we construct a new hyperplane for single-valued variational inequality and propose a class of double projection algorithms without monotonicity.Under the condition that the solution set of the dual variational inequality is not empty and the mapping is continuous,the convergence of the algorithm is proved.Secondly,for the set-valued variational inequality,a class of projection algorithms is given for set-valued variational inequality without monotonicity.The convergence of the algorithm is proved under the condition that the solution set of dual variational inequality is not empty and the mapping is continuous,compact and convex.