A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem
A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem
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DOI：
10.1007/s10957-021-01839-6
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发表时间：
2021-03
影响因子：
1.9
通讯作者：
Jingyong Tang;Hongchao Zhang
中科院分区：
文献类型：
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作者：
Jingyong Tang;Hongchao Zhang
加权互补问题（WCP）是一般互补问题的一个重要推广，可用于对更大类的科学和工程问题进行建模。本文通过引入一类包含权向量的单参数光滑函数，提出了一种非单调线搜索的光滑牛顿算法来求解WCP问题。我们表明，该算法产生的迭代的任何聚点，如果存在，是所考虑的WCP的解决方案。此外，当WCP的解集非空时，在弱于Jacobian非奇异性假设的条件下，我们证明了该算法产生的迭代序列是有界的，并且以局部超线性或二次收敛速度收敛于WCP的一个解.还报道了有希望的数值结果。
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.