A modified multivariate spectral gradient projection method for nonlinear complementarity problems

We present a sufficient condition for monotonicity of the nonlinear nonsmooth system generated by Fischer–Burmeister function associated with nonlinear complementarity problem. Based on the presented condition, the nonlinear complementarity problem considered in this paper is equivalently formulated to a nonsmooth monotone system. We then propose a modified multivariate spectral gradient projection method for the resulting system, and establish the global convergence without smoothness and Lipschitz condition. Preliminary numerical experiments show that, compared to some existing methods, the proposed method is effective.