The Solution Of Variational Inequality Problem And Perturbation Analysis Of Projection Algorithm

This paper mainly studies the algorithms for variational inequality problem and perturbation analysis of projection algorithms. Projection algorithms for variational inequalities have been extensively studied. At present, double projection algorithm is one of the most effective method of projection algorithms. Projection operation is very important to projection algorithms. Frequently, projection operation are unable to solve exactly. So we prove that the double projection algorithm after perturbation is well-defined and the generated sequence converges to a solution. Solodov and Svaiter propose a hybrid projection-proximal point algorithm for finding zeros of a maximal monotone operator. In the third part of this paper, we use hybrid projection-proximal algorithm to solve variational inequality problem with pseudo-monotone mapping; and prove that the iterate sequence produced by hybrid projection-proximal point algorithm with perturbation is convergent. A few researchers concerned the subproblem of proximal point algorithm. In the last part, using the idea of double projection method, we propose a method for solving it.