A fixed-point method for a class of super-large scale nonlinear complementarity problems

作者：Zhao Jian Xun^*

来源：Computers & Mathematics with Applications, 2014, 67(5): 999-1015.

DOI：10.1016/j.camwa.2014.01.011

• Fixed-point algorithm
• Absolute value equations
• Smoothing function
• Global convergence
• Q-linear convergence

We consider a class of complementarity problems involving functions which are nonlinear. In this paper we reformulate this nonlinear complementarity problem as a system of absolute value equations (which is nonsmooth). Then we propose a fixed-point method to solve this nonsmooth system. We prove that the proposed method is globally linearly convergent under a mild condition. The proposed method is greatly effective not only for small and medium size problems, but also for large and super-large scale problems. Especially, our method can efficiently solve super-large scale problems, with a million variables, in a few tens of minutes on a PC.

• 出版日期2014-3
• 单位天津大学