Convergence analysis of iterative methods for some variational inequalities with pseudomonotone operators
The authors consider variational inequalities of the second kind with a pseudomonotone operator and a convex nondifferentiable functional in Banach spaces. A two-layer iterative method is proposed for solvability, which reduces the original variational inequality to one with a duality operator that has better properties than the original operator. The convergence of the iterative process is analyzed. In particular, it is shown that the iterative sequence is bounded and each of its weak limit point is a solution of the original inequality. In the case of a Hilbert space, weak convergence is proved of the entire iterative sequence under suitable additional requirements.
scientific article; zbMATH DE number 1758768