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

Bergou, El Houcine; Diouane, Youssef; Kungurtsev, Vyacheslav; Royer, Clément W. (2021), A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems, SIAM Journal on Scientific Computing, 43, 5, p. S743-S766. 10.1137/20M1349138

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Bergou_28278.pdf (1.051Mb)
Type
Article accepté pour publication ou publié
Date
2021
Journal name
SIAM Journal on Scientific Computing
Volume
43
Number
5
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
S743-S766
Publication identifier
10.1137/20M1349138
Metadata
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Author(s)
Bergou, El Houcine
Diouane, Youssef
Kungurtsev, Vyacheslav
Royer, Clément W.
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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.
Subjects / Keywords
Nonlinear least squares; Equality constraints; Levenberg-Marquardt method; Iterative linear algebra; PDE-constrained optimization

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