An augmented Lagrangian algorithm for constrained nonlinear least-squares
Optimization and Control
2026-07-13 v1 Numerical Analysis
Abstract
We present an algorithm for solving nonlinear least-squares problems subject to a mix of nonlinear and linear constraints. The nonlinear constraints are handled by reformulating the objective as the augmented Lagrangian function while linear constraints are handled directly. Each iteration consists of approximately solving a linearly constrained problem by means of a gradient projection technique. Our approach also involves a structured approximation of the augmented Lagrangian Hessian. We show global convergence of the method and assess the performance through numerical experiments.
Cite
@article{arxiv.2607.11239,
title = {An augmented Lagrangian algorithm for constrained nonlinear least-squares},
author = {Pierre Borie and Fabian Bastin and Stéphane Dellacherie},
journal= {arXiv preprint arXiv:2607.11239},
year = {2026}
}