A proximal decomposition algorithm for variational inequality problems

作者：Han DR^*

来源：Journal of Computational and Applied Mathematics, 2003, 161(1): 231-244.

DOI：10.1016/j.cam.2003.08.001

• variational inequality problems
• decomposition algorithms
• global convergence
• monotone mappings

In this paper, we propose a new decomposition algorithm for solving monotone variational inequality problems with linear constraints. The algorithm utilizes the problem';s structure conductive to decomposition. At each iteration, the algorithm solves a system of nonlinear equations, which is structurally much easier to solve than variational inequality problems, the subproblems of classical decomposition methods, and then performs a projection step to update the multipliers. We allow to solve the subproblems approximately and we prove that under mild assumptions on the problem';s data, the algorithm is globally convergent. We also report some preliminary computational results, which show that the algorithm is encouraging.

• 出版日期2003-12-1
• 单位南京师范大学