Abstract: In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.
Abstract: In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.
Abstract: In this paper, the difference between the Alternating
Direction Method (ADM) and the Non-Splitting Method (NSM) is
investigated, while both methods applied to the simulations for 2-D
multimaterial radiation diffusion issues. Although the ADM have the
same accuracy orders with the NSM on the uniform meshes, the
accuracy of ADM will decrease on the distorted meshes or the
boundary of domain. Numerical experiments are carried out to
confirm the theoretical predication.