A hybrid splitting method for variational inequality problems with separable structure

作者：He, Hongjin; Han, Deren; Sun, Wenyu^*; Chen, Yannan

来源：Optimization Methods and Software, 2013, 28(4): 725-742.

DOI：10.1080/10556788.2011.633609

• splitting method
• alternating direction method
• nonlinear equations
• variational inequality problems
• separable structure

Alternating direction method (ADM), which decomposes a large-scale original variational inequality (VI) problem into a series of smaller scale subproblems, is very attractive for solving a class of VI problems with a separable structure. This type of method can greatly improve the efficiency, but cannot avoid solving VI subproblems. In this paper, we propose a hybrid splitting method with variable parameters for separable VI problems. Specifically, the proposed method solves only one strongly monotone VI subproblem and a well-posed system of nonlinear equations in each iteration. The global convergence of the new method is established under some standard assumptions as those in classical ADMs. Finally, some preliminary numerical results show that the proposed method performs favourably in practice.

• 出版日期2013-8-1
• 单位南京师范大学; 南京林业大学