A Self-adaptive Alternating Direction Method For Solving Structured Variational Inequalities

Alternating direction method is an effective method for solving struc-tured monotone variational inequalities.It is a decomposition method to obtain the solution of the original problem via alternately solving a se-ries of sub-problems.We propose a descent method for solving structured monotone variational inequalities with self-adaptive penalty parameters.The method is based on the descent method presented by Yuan Xiao Ming[Comput Optim Appl(2011)49:17-29],and use self-adaptive penalty parameters' adjustment rules.Under reasonable assumptions,we can prove its convergence.Numerical tests show that our algorithm needs less number of iterations than the original algorithm.