OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients

Bellavia, Stefania and Gratton, Serge and Riccietti, Elisa A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. (2018) Numerische Mathematik, 140 (3). 791-825. ISSN 0029-599X

[img]
Preview
(Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
663kB

Official URL: https://doi.org/10.1007/s00211-018-0977-z

Abstract

In this paper we consider large scale nonlinear least-squares problems for which function and gradient are evaluated with dynamic accuracy and propose a Levenberg-Marquardt method for solving such problems. More precisely, we consider the case in which the exact function to optimize is not available or its evaluation is computationally demanding, but approximations of it are available at any prescribed accuracy level. The proposed method relies on a control of the accuracy level, and imposes an improvement of function approximations when the accuracy is detected to be too low to proceed with the optimization process. We prove global and local convergence and complexity of our procedure and show encouraging numerical results on test problems arising in data assimilation and machine learning.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Università degli Studi di Firenze (ITALY)
Laboratory name:
Statistics:download
Deposited On:03 Mar 2020 13:26

Repository Staff Only: item control page