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Main Authors: Bellavia, Stefania, Malaspina, Greta, Morini, Benedetta
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2506.03965
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author Bellavia, Stefania
Malaspina, Greta
Morini, Benedetta
author_facet Bellavia, Stefania
Malaspina, Greta
Morini, Benedetta
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_03965
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A variable dimension sketching strategy for nonlinear least-squares
Bellavia, Stefania
Malaspina, Greta
Morini, Benedetta
Optimization and Control
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.
title A variable dimension sketching strategy for nonlinear least-squares
topic Optimization and Control
url https://arxiv.org/abs/2506.03965