关键词: 椭圆型方程, Robin反问题, 增广拉格朗日方法, 正则化

Abstract: 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.

Key words: elliptic equations, Robin inverse problem, augmented Lagrangian method, regularization