A globally and superlinearly convergent smoothing Broyden-like method for solving nonlinear complementarity problem

作者：Ma, Changfeng^*; Chen, Linjie; Wang, Desheng

来源：Applied Mathematics and Computation, 2008, 198(2): 592-604.

DOI：10.1016/j.amc.2007.08.057

• nonlinear complementarity problem
• smoothing Broyden-like method
• global convergence
• superlinear convergence

The nonlinear complementarity problem (denoted by NCP(F)) has attracted much attention due to its various applications in economics, engineering and management science. In this paper, we propose a smoothing Broyden-like method for solving nonlinear complementarity problem. The algorithm considered here is based on the smooth approximation Fischer - Burmeister function and makes use of the derivative-free line search rule of Li in [D. H. Li, M. Fukushima, A derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optim. Meth. Software 13(3) (2000) 181 - 201]. We show that, under suitable conditions, the iterates generated by the proposed method converge to a solution of the nonlinear complementarity problem globally and superlinearly.

• 出版日期2008-5-1
• 单位桂林电子科技大学; 南阳理工学院; 福建师范大学