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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00351349" target="_blank" >RIV/68407700:21230/21:00351349 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/20M1349138" target="_blank" >https://doi.org/10.1137/20M1349138</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/20M1349138" target="_blank" >10.1137/20M1349138</a>

Result language
angličtina
Original language name
A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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