A NONMONOTONE MATRIX-FREE ALGORITHM FOR NONLINEAR EQUALITY-CONSTRAINED LEAST-SQUARES PROBLEMS


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Output type: Journal article

UM6P affiliated Publication?: Yes

Author list: Bergou, El Houcine; Diouane, Youssef; Kungurtsev, Vyacheslav; Royer, Clement W.

Publisher: Society for Industrial and Applied Mathematics

Publication year: 2021

Journal: SIAM Journal on Scientific Computing (1064-8275)

Volume number: 43

Issue number: 5

Start page: S743

End page: S766

ISSN: 1064-8275

eISSN: 1095-7197

URL: https://epubs.siam.org/doi/abs/10.1137/20M1349138

Languages: English (EN-GB)


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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 Levenb erg-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.


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Last updated on 2022-14-01 at 23:22