We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and inexact Newton methods for nonlinear systems of equations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented.

翻译：我们开发并分析了用于非线性最小二乘问题的随机不精确高斯-牛顿方法以及用于非线性方程组的随机不精确牛顿方法。通过采用合适的采样策略构建确定性模型中相关矩阵的随机近似，形成随机模型。针对一阶最优性条件，在最坏情况下达到期望精度所需迭代次数的期望分析，为如何施加采样策略——以固定概率确保随机近似具有适当的精度——提供了指导准则。本文还给出了算法的数值验证结果。