Levenberg-Marquardt method based on probabilistic Jacobian models for nonlinear equations

作者：Zhao, Ruixue; Fan, Jinyan^*

来源：Computational Optimization and Applications, 2022, 83(2): 381-401.

DOI：10.1007/s10589-022-00393-9

• Levenberg-Marquardt method
• Probabilistic Jacobian models
• Derivative-free optimization
• Global convergence

In this paper, we propose a Levenberg-Marquardt method based on probabilistic models for nonlinear equations for which the Jacobian cannot be computed accurately or the computation is very expensive. We introduce the definition of the first-order accurate probabilistic Jacobian model, and show how to construct such a model with sample points generated by standard Gaussian distribution. Under certain conditions, we prove that the proposed method converges to a first order stationary point with probability one. Numerical results show the efficiency of the method.

• 单位
  上海交通大学