基于一个新的NCP函数的光滑牛顿法求解变分不等式问题
Smooth Newton Method Based on a New NCP Function for Solving Variational Inequality Problems
摘要: 本文研究了变分不等式KKT系统的求解问题，利用一个新的NCP函数将变分不等式的KKT条件转化为等价的光滑方程组。并在此建立了求解NCP函数非线性互补问题的一个光滑化牛顿法，获得算法的收敛性和局部收敛性结果，并给出数值实验结果验证理论分析的准确性。
Abstract: In this paper, we study the solution of the variational inequality KKT systems. A new NCP function is used to convert KKT conditions of variational inequalities into an equivalent smooth equation. And a smoothing Newton method for solving the nonlinear complementarity problem of NCP function is established, and the convergence and local convergence of the algorithm are obtained, and the accuracy of the theoretical analysis is verified by numerical experiments.
文章引用：贾春阳, 孙菊贺, 杨峥. 基于一个新的NCP函数的光滑牛顿法求解变分不等式问题[J]. 应用数学进展, 2017, 6(9): 1220-1228. https://doi.org/10.12677/AAM.2017.69147

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