The weighted complementarity problem (denoted by WCP) significantly extends the general complementarity problem and can be used for modeling a larger class of problems from science and engineering. In this paper, by introducing a one-parametric class of smoothing functions which includes the weight vector, we propose a smoothing Newton algorithm with nonmonotone line search to solve WCP. We show that any accumulation point of the iterates generated by this algorithm, if exists, is a solution of the considered WCP. Moreover, when the solution set of WCP is nonempty, under assumptions weaker than the Jacobian nonsingularity assumption, we prove that the iteration sequence generated by our algorithm is bounded and converges to one solution of WCP with local superlinear or quadratic convergence rate. Promising numerical results are also reported.

加权互补问题（由WCP表示）极大地扩展了一般的互补问题，可用于对科学和工程学中的较大类问题进行建模。在本文中，通过引入一类包含权重向量的平滑函数，我们提出了一种具有非单调线搜索的平滑牛顿算法来求解WCP。我们表明，此算法生成的迭代的任何累加点（如果存在）都是考虑的WCP的解决方案。此外，当WCP的解集为非空时，在比Jacobian非奇异性假设弱的假设下，我们证明了我们算法生成的迭代序列是有界的，并且收敛到具有局部超线性或二次收敛率的WCP的一个解。还报告了有希望的数值结果。