Abstract: We proposed a new inexact nonmonotone smoothing Newton method for the linear weighted second-order cone complementarity problem. Firstly, based on a new smoothing function with parameters, the linear weighted second-order cone complementarity problem was transformed into a system of smooth equations. Secondly, we gave a new inexact nonmonotone smoothing Newton method for solving the equations. Finally, under the assumption of positive semidefinite matrix, we proved the global convergence and local superlinear convergence of the algorithm. Some numerical results show that the algorithm is stable and effective.

Key words: linear weighted second-order cone complementarity problem, inexact smoothing Newton method, nonmonotone line search, global convergence, local superlinear convergence