论文标题
在Levenberg-Marquardt方法中选择Lagrange乘数的范围重汇标准
Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg-Marquardt method
论文作者
论文摘要
在本文中，我们提出了一种新的策略，用于在Levenberg-Marquardt方法中选择Lagrange乘数，以解决由非线性操作员在Hilbert Space之间作用的非线性操作员建模的不良问题。为提出的方法建立了收敛分析结果，包括：迭代误差的单调性，残差的几何衰减，噪声数据的精确数据的收敛性，稳定性和半对流。提出了数值实验，以进行椭圆参数识别二维EIT问题。将我们策略的性能与Levenberg-Marquardt方法的标准实现进行了比较（使用乘数的先验选择）。
In this article we propose a novel strategy for choosing the Lagrange multipliers in the Levenberg-Marquardt method for solving ill-posed problems modeled by nonlinear operators acting between Hilbert spaces. Convergence analysis results are established for the proposed method, including: monotonicity of iteration error, geometrical decay of the residual, convergence for exact data, stability and semi-convergence for noisy data. Numerical experiments are presented for an elliptic parameter identification two-dimensional EIT problem. The performance of our strategy is compared with standard implementations of the Levenberg-Marquardt method (using a priori choice of the multipliers).
