A new alternating direction method for co-coercive variational inequality problems

作者：Zhang Wenxing; Han Deren^*

来源：Computers & Mathematics with Applications, 2009, 57(7): 1168-1178.

DOI：10.1016/j.camwa.2008.09.049

• Variational inequality problems
• Co-coercive mappings
• Projection methods
• Alternating direction methods

This paper presents a new alternating direction method for solving co-coercive variational inequality problems, where the feasible set is the intersection of a simple set and polyhedron defined by a system of linear equations. The proposed method can be viewed as a combination of Han and Lo';s alternating direction method [D.R. Han, H.K. Lo, A new alternating direction method for a class of nonlinear variational inequality problems, journal of Optimization Theory and Applications 112 (3) (2002) 549-560] for such class of variational inequality problems and Li, Liao and Yuan';s modified descent method for co-coercive variational inequality problems [M. Li, LZ. Liao, X.M. Yuan, A modified descent projection method for co-coercive variational inequalities, European Journal of Operational Research 189 (2) (2008) 310-323]. Thus, it possesses the advantages of both Han and Lo';s alternating direction method, which solves a series of small-scale easier problems to solve the original variational inequality problem, and Li, Liao and Yuan';s modified descent method, which is simple provided that the feasible set is simple. We test the new method and compare it with Han and Lo';s method and Li, Liao and Yuan';s modified descent method, and the numerical results show that our new method is suitable for such class of variational inequality problems.

• 出版日期2009-4
• 单位南京师范大学