Global Convergence of a Stochastic Levenberg–Marquardt Algorithm Based on Trust Region

In this paper, we propose a stochastic Levenberg–Marquardt algorithm based on trust region for stochastic nonlinear least squares problems, where the stochastic Jacobians and gradients are used instead of the exact Jacobians and gradients. We show that the estimates and models of the objective function are probabilistically accurate if the number of samples at each iteration is chosen appropriately. Further, we prove that at least one accumulation point of the sequence generated by the proposed algorithm is a stationary point of the objective function with probability one.