关键词: 线性二阶锥权互补问题, 非精确光滑化牛顿法, 非单调线搜索, 全局收敛, 局部超线性收敛

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