Abstract: We presented a new smoothing Newton method for solving the linear circular cone complementarity problems. Firstly, based on  the smoothing function of the circular cone complementary function, the linear circular cone complementarity problem was transformed into a system of equations, which were solved by the smoothing Newton method. Secondly, under suitable assumptions, we proved that the algorithm had the global convergence and local quadratic convergence. The numerical results show that the CPU time and iteration times of the algorithm for solving linear circular cone complementarity problems are less, and the algorithm is relatively stable, which proves the effectiveness of the algorithm.

Key words: linear circular cone complementarity problem, smoothing Newton method, smoothing function, global convergence, local quadratic convergence