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A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems

Bergou, El Houcine and Diouane, Youssef and Kungurtsev, Vyacheslav and Royer, Clément W. A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems. (2021) SIAM Journal on Scientific Computing. S743-S766. ISSN 1064-8275

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Official URL: https://doi.org/10.1137/20M1349138

Abstract

Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must account for nonlinear dynamics by incorporating constraints. In addition, these systems often incorporate a large number of variables, which increases the difficulty of the problem, and motivates the need for efficient algorithms amenable to large-scale implementations. In this paper, we propose and analyze a Levenberg-Marquardt algorithm for nonlinear least squares subject to nonlinear equality constraints. Our algorithm is based on inexact solves of linear least-squares problems, that only require Jacobian-vector products. Global convergence is guaranteed by the combination of a composite step approach and a nonmonotone step acceptance rule. We illustrate the performance of our method on several test cases from data assimilation and inverse problems: our algorithm is able to reach the vicinity of a solution from an arbitrary starting point, and can outperform the most natural alternatives for these classes of problems.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Université Paris Sciences & Lettres - PSL (FRANCE)
Other partners > Czech Technical University in Prague - CTU (CZECH REPUBLIC)
Other partners > Université Mohammed VI Polytechnique (MOROCCO)
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Deposited On:14 Sep 2021 07:26

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