A variable dimension sketching strategy for nonlinear least-squares
Abstract
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model. Under suitable assumptions on the objective function and the random subspace, we prove a probabilistic bound on the number of iterations needed to drive the norm of the gradient below any given threshold. Moreover, we provide a theoretical analysis of the local behavior of the method. The numerical experiments demonstrate the effectiveness of the proposed method.
Cite
@article{arxiv.2506.03965,
title = {A variable dimension sketching strategy for nonlinear least-squares},
author = {Stefania Bellavia and Greta Malaspina and Benedetta Morini},
journal= {arXiv preprint arXiv:2506.03965},
year = {2025}
}