青岛大学学报（自然科学版）2026，Vol.39Issue(3)：3-8,6.DOI:10.3969/j.issn.1006-1037.2026.03.02
求解非线性互补问题的非精确光滑化牛顿算法
Inexact Smoothing Newton Algorithm for Nonlinear Complementarity Problems
摘要
Abstract
When using traditional Newton's method to solve large-scale nonlinear comple-mentarity problems,accurately solving linear subsystems significantly increases computa-tional complexity,while matrix inversion and storage requirements also become the main bottlenecks restricting algorithm efficiency.Therefore,an inexact smoothing Newton algorithm based on smooth symmetric perturbation functions was proposed.By introdu-cing an inexact solution strategy and an adaptive parameter adjustment mechanism,the computational cost is significantly reduced while ensuring global superlinear convergence(local quadratic convergence).Numerical experiments show that the algorithm proposed reduces the number of iterations by 40%to 60%compared to classical methods when sol-ving problems with dimensions over a thousand.关键词
非线性互补问题/光滑化方法/非精确光滑化牛顿法/自适应参数/局部二次收敛Key words
nonlinear complementarity problem/smoothing method/inexact smoothing Newton algorithm/adaptive parameters/local quadratic convergence分类
数理科学引用本文复制引用
朱子旋,芮绍平..求解非线性互补问题的非精确光滑化牛顿算法[J].青岛大学学报（自然科学版）,2026,39(3):3-8,6.基金项目
安徽省教育厅自然科学研究项目(批准号:2023AH050348,2023ZK027,2023ZK030)资助. （批准号:2023AH050348,2023ZK027,2023ZK030）
