Solving a class of asymmetric variational inequalities by a new alternating direction method

✍ Scribed by Shengli Wang; Hai Yang; Bingsheng He

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 549 KB
• Volume: 40
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(00)85004-x

✦ Synopsis

The augmented Lagrangian method (also referred to as an alternating direction method) solves a class of variational inequalities (VI) via solving a series of sub-VI problems. The method is effective whenever the subproblems can be solved efficiently. However, the subproblem to be solved in each iteration of the augmented Lagrangian method itself is still a VI problem. It is essentially as difficult as the original one, the only difference is that the dimension of the subproblems is lower, In this paper, we propose a new alternating direction method for solving a class of monotone variational inequalities. In each iteration, the method solves a convex quadratic programming with simple constrains and a well-conditioned system of nonlinear equations. For such 'easier' subproblems, existing efficient numerical softwares are applicable. The effectiveness of the proposed method is demonstrated with an illustrative example.