We consider the weighted linear complementarity problem (denoted by wLCP). Many numerical algorithms have been proposed for solving the monotone wLCP. In this paper, we propose a damped Gauss–Newton method to solve the non-monotone wLCP which is designed based on a derivative-free non-monotone line search. We show that the proposed method is well defined and it is globally convergent without any problem assumptions. Moreover, we analyze the local quadratic convergence of the proposed method under the non-singularity condition and the local error bound condition, respectively. Our method not only has encouraging local convergence properties but also can be used to solve non-monotone wLCPs. Preliminary numerical results are reported.

我们考虑加权线性互补问题（由 wLCP 表示）。已经提出了许多数值算法来解决单调 wLCP。在本文中，我们提出了一种阻尼 Gauss-Newton 方法来解决基于无导数非单调线搜索设计的非单调 wLCP。我们表明，所提出的方法定义明确，并且在没有任何问题假设的情况下具有全局收敛性。此外，我们分别分析了该方法在非奇点条件和局部误差界限条件下的局部二次收敛性。我们的方法不仅具有令人鼓舞的局部收敛特性，而且可用于解决非单调 wLCP。报告了初步的数值结果。