A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem

作者：Fan, Xiaona^*; Yan, Qinglun

来源：Asia Pacific Journal of Operational Research, 2018, 35(4): 1850027.

DOI：10.1142/S0217595918500276

• Nonlinear complementarity problem
• smoothing homotopy method
• smoothing function
• global convergence

In this paper, we propose a new proof for smoothing homotopy method based on the Fischer-Burmeister function to solve the nonlinear complementarity problem under a nonmonotone solution condition. Under this assumption condition imposed on the defined mapping F, global convergence of a smooth curve determined by the referred homotopy equation is established for almost all initial points in R-+(n) and it is actually regarded as an interior point met hod. Besides, if the initial point is expanded to R-n, the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems.

• 出版日期2018-8
• 单位南京邮电大学