Skip to main content
SpringerLink
Log in

Adaptive Gauss–Newton Method for Solving Systems of Nonlinear Equations

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

For systems of nonlinear equations, we propose a new version of the Gauss–Newton method based on the idea of using an upper bound for the residual norm of the system and a quadratic regularization term. The global convergence of the method is proved. Under natural assumptions, global linear convergence is established. The method uses an adaptive strategy to choose hyperparameters of a local model, thus forming a flexible and convenient algorithm that can be implemented using standard convex optimization techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. A. I. Golikov, Yu. G. Evtushenko, and I. E. Kaporin, Comput. Math. Math. Phys. 59 (12), 2017–2032 (2019). https://doi.org/10.1134/S0044466919120093.

    Article  MathSciNet  Google Scholar 

  2. Yu. Nesterov, Lectures on Convex Optimization (Springer, Berlin, 2018).

    Book  Google Scholar 

  3. A. V. Gasnikov, Modern Numerical Optimization Methods: Universal Gradient Descent (Mosk. Tsentr Neprer. Mat. Obrazovan., Moscow, 2020) [in Russian].

    Google Scholar 

  4. Yu. Nesterov, Optim. Methods Software 22 (3), 469–483 (2007).

    Article  MathSciNet  Google Scholar 

  5. E. Gorbunov, F. Hanzely, and P. Richtárik, “A unified theory of SGD: Variance reduction, sampling, quantization and coordinate descent,” International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research (2020), pp. 680–690.

  6. B. T. Polyak, USSR Comput. Math. Math. Phys. 3 (4), 864–878 (1963).

    Article  Google Scholar 

  7. Yu. Nesterov, “Flexible modification of Gauss–Newton method,” CORE Discussion Papers (2021).

    Google Scholar 

  8. N. Yudin and A. Gasnikov, Preprint No. 2813 (WIAS, 2021). https://doi.org/10.20347/wias.preprint.2813

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 21-71-30005.

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia

    N. E. Yudin

  2. Federal Research Center “Informatics and Control,” Russian Academy of Sciences, Moscow, Russia

    N. E. Yudin

Authors
  1. N. E. Yudin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. E. Yudin.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yudin, N.E. Adaptive Gauss–Newton Method for Solving Systems of Nonlinear Equations. Dokl. Math. 104, 293–296 (2021). https://doi.org/10.1134/S1064562421050161

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562421050161

Keywords:

Search

Navigation