A simple self-adaptive alternating direction method for linear variational inequality problems

In this study, we propose a new alternating direction method for solving linear variational variational inequality problems (LVIP). It is simple in the sense that, at each iteration, it needs only to perform a projection onto a simple set and some matrix–vector multiplications. The simplicity of the solution method makes it attractive for solving large-scale problems. To further improve its efficiency, we devise a self-adaptive strategy for choosing the necessary parameters of the solution procedure. We prove the global convergence of this new method under some mild conditions. Finally, some computational results are reported to demonstrate the properties and efficiency of the method.