Robin系数辨识的增广拉格朗日方法  

An Augmented Lagrangian Method for Identifying Robin Coefficient

作　　者：贺佳庆 刘杰[1] HE Jiaqing;LIU Jie(School of Mathematical and Physical Sciences,Wuhan Textile University,Wuhan 430200,Hubei,China)

机构地区：[1]武汉纺织大学数理科学学院,湖北武汉430200

出　　处：《江汉大学学报（自然科学版）》2024年第6期29-36,共8页Journal of Jianghan University：Natural Science Edition

基　　金：国家自然科学基金面上项目(61573011)。

摘　　要：提出了一种基于解在可测边界上的测量值来估计椭圆型方程中Robin系数的非线性反问题。首先应用正则化方法将该反问题转化为带约束的极小值问题,并且证明了极小解的存在性。然后应用增广拉格朗日方法将该带约束的极小值问题转化为无约束的鞍点问题,并且在理论上严格证明了它们的等价性。A nonlinear inverse problem was proposed to estimate Robin coefficients in elliptic equations based on the measured values of the solution on measurable boundaries.Firstly,the regularization method was applied to transform the inverse problem into a constrained minimum problem,and the existence of the minimization solution was proved.Then,the augmented Lagrangian method was used to convert the constrained minimum problem into an unconstrained saddle point problem,and their equivalence was proved strictly in theory.

关 键 词：椭圆型方程 Robin反问题 增广拉格朗日方法 正则化 

分 类 号：O175.25[理学—数学]