应用数学和力学2025，Vol.46Issue(7)：916-925,10.DOI:10.21656/1000-0887.450171
求解两区域变分不等式的自适应交替方向乘子法
A Self-Adaptive Alternating Direction Multiplier Method for Variational Inequality in 2 Domains
摘要
Abstract
A self-adaptive alternating direction multiplier method was proposed for a class of contact problems defined in 2 domains.A minimization problem constrained by inequalities was obtained for the variational prob-lem in 2 domains,then the problem was equivalent to a saddle-point problem through introduction of an auxilia-ry unknown on the contact boundary.The alternating direction multiplier method was applied to the saddle point problem for the numerical solution,with each iteration successively determining the auxiliary variable ex-plicitly,solving a linear problem and updating the Lagrange multiplier.The self-adaptive alternating direction multiplier method was proposed to select the penalty parameter automatically,by means of a self-adaptive rule and iterative functions.The results prove the convergence and demonstrate the effectiveness of the proposed method.关键词
变分不等式/鞍点问题/交替方向乘子法/自适应罚参数Key words
variational inequality/saddle point problem/alternating direction multiplier method/self-adaptive penalty parameter分类
数理科学引用本文复制引用
袁星月,崔席勇,冉瑞生,张守贵..求解两区域变分不等式的自适应交替方向乘子法[J].应用数学和力学,2025,46(7):916-925,10.基金项目
国家自然科学基金(11971085) 本文作者衷心感谢中冶集团"181计划"研发项目(90310365)对本文的资助. （11971085）
