Two kinds of conjugate gradient methods for solving nonlinear complementarity problems

In this paper, we use the Fischer-Burmeister function to reformulate the nonlinear complementarity problems as a system of nonsmooth equation. By analysing the properties of merit function, we propose two kinds of conjugate gradient methods for solving the nonlinear complementarity problems under two Armijo-type line searches. The methods can guarantee the sufficient descent property and the global convergence. Finally, some numerical tests are also given.