Convergence Of Inexact Proximal Point Algorithm For General Variational Inequalities

For variational inequalities in Hilbert space transform it into variational inclusion problem equivalently. Then use inexact proximal point algorithm to solve the problem.Firstly, propose a new error criterion. Proof this algorithm is convergent globally under the new criterion. Under the conditions that the operator F is g-monotone and the operator g is homeomorphism get the conclusion that the inexact proximal point algorithm converges to a solution of general variational inequalities and this solution is unique.Secondly, propose a modified inexact proximal point algorithm for general variational inequalities. The modified algorithm provides the correction step and estimation step the standard of length step. The size of step is easily to be calculated. It reduces the calculation of the projector when generating the next iteration. Finally, prove that the algorithm converges to a solution of general variational inequalities under the conditions that operator F is g-monotone and the operator g is the homeomorphism.