IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v463y2024ics0096300323005349.html
   My bibliography  Save this article

Convergence properties of Levenberg–Marquardt methods with generalized regularization terms

Author

Listed:
  • Ariizumi, Shumpei
  • Yamakawa, Yuya
  • Yamashita, Nobuo

Abstract

Levenberg–Marquardt methods (LMMs) are the most typical algorithms for solving nonlinear equations F(x)=0, where F:Rn→Rm is a continuously differentiable function. They sequentially solve subproblems represented as squared residual of the Newton equations with the L2 regularization to determine the search direction. However, since the subproblems of the LMMs are usually reduced to linear equations with n variables, it takes much time to solve them when m≪n.

Suggested Citation

  • Ariizumi, Shumpei & Yamakawa, Yuya & Yamashita, Nobuo, 2024. "Convergence properties of Levenberg–Marquardt methods with generalized regularization terms," Applied Mathematics and Computation, Elsevier, vol. 463(C).
  • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005349
    DOI: 10.1016/j.amc.2023.128365
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323005349
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2023.128365?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    2. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richard Pierse, 2006. "Optimal control in nonlinear models: a generalised Gauss-Newton algorithm with analytic derivatives," School of Economics Discussion Papers 0906, School of Economics, University of Surrey.
    2. Andrew Patton, 2002. "(IAM Series No 001) On the Out-Of-Sample Importance of Skewness and Asymetric Dependence for Asset Allocation," FMG Discussion Papers dp431, Financial Markets Group.
    3. Francisco Gallego & Andrés Hernando, 2009. "School Choice in Chile: Looking at the Demand Side," Documentos de Trabajo 356, Instituto de Economia. Pontificia Universidad Católica de Chile..
    4. Claude Hillinger, 2002. "A General Theory of Price and Quantity Aggregation and Welfare Measurement," CESifo Working Paper Series 818, CESifo.
    5. Salerno, Gillian & Beard, Rodney & McDonald, Stuart, 2007. "Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes," MPRA Paper 11225, University Library of Munich, Germany, revised 22 Oct 2008.
    6. Maria Casanova-Rivas, 2008. "Dynamic Complementarities: A Computational and Empirical Analysis of Couples' Retirement Decisions," 2008 Meeting Papers 1073, Society for Economic Dynamics.
    7. Heer, Burkhard & Polito, Vito & Wickens, Michael R., 2020. "Population aging, social security and fiscal limits," Journal of Economic Dynamics and Control, Elsevier, vol. 116(C).
    8. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    9. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    10. Pelin Ilbas, 2006. "Optimal Monetary Policy rules for the Euro area in a DSGE framework," Working Papers of Department of Economics, Leuven ces0613, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    11. Atanas Christev, 2006. "Learning Hyperinflations," Computing in Economics and Finance 2006 475, Society for Computational Economics.
    12. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers.
    13. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    14. Frölich, Markus & Lechner, Michael, 2010. "Exploiting Regional Treatment Intensity for the Evaluation of Labor Market Policies," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1014-1029.
    15. Nikolaj Malchow-Møller & Michael Svarer, 2003. "Estimation of the multinomial logit model with random effects," Applied Economics Letters, Taylor & Francis Journals, vol. 10(7), pages 389-392.
    16. Röhrs, Sigrid & Winter, Christoph, 2017. "Reducing government debt in the presence of inequality," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 1-20.
    17. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
    18. Wieland, Volker, 2000. "Monetary policy, parameter uncertainty and optimal learning," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 199-228, August.
    19. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    20. Adam, Klaus & Billi, Roberto M., 2006. "Optimal Monetary Policy under Commitment with a Zero Bound on Nominal Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(7), pages 1877-1905, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005349. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.