IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v91y2025i1d10.1007_s10589-025-00665-0.html
   My bibliography  Save this article

Speeding up L-BFGS by direct approximation of the inverse Hessian matrix

Author

Listed:
  • Ashkan Sadeghi-Lotfabadi

    (Ferdowsi University of Mashhad)

  • Kamaledin Ghiasi-Shirazi

    (Ferdowsi University of Mashhad)

Abstract

L-BFGS is one of the widely used quasi-Newton methods. Instead of explicitly storing an approximation H of the inverse Hessian, L-BFGS keeps a limited number of vectors that can be used for computing the product of H by the gradient. However, this computation is sequential, each step depending on the outcome of the previous step. To solve this problem, we propose the Direct L-BFGS (DirL-BFGS) method that, seeing H as a linear operator, directly stores a low-rank plus diagonal (LRPD) representation of H. Employing the LRPD representation enables us to leverage the benefits of vector processing, leading to accelerating and parallelizing the calculations in the form of single instruction, multiple data. We evaluate our proposed method on different quadratic optimization problems and several regression and classification tasks with neural networks. Numerical results show that DirL-BFGS is faster overall than L-BFGS.

Suggested Citation

  • Ashkan Sadeghi-Lotfabadi & Kamaledin Ghiasi-Shirazi, 2025. "Speeding up L-BFGS by direct approximation of the inverse Hessian matrix," Computational Optimization and Applications, Springer, vol. 91(1), pages 283-310, May.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:1:d:10.1007_s10589-025-00665-0
    DOI: 10.1007/s10589-025-00665-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-025-00665-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-025-00665-0?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. Kelley Pace, R. & Barry, Ronald, 1997. "Sparse spatial autoregressions," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 291-297, May.
    2. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    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. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    2. Alexandre Xavier Ywata Carvalho & Pedro Henrique Melo Albuquerque & Gilberto Rezende de Almeida Junior & Rafael Dantas Guimarães & Camilo Rey Laureto, 2009. "Clusterização Hierárquica Espacial com Atributos Binários," Discussion Papers 1428, Instituto de Pesquisa Econômica Aplicada - IPEA.
    3. Lavado, Rouselle F. & Barrios, Erniel B., 2010. "Spatial Stochastic Frontier Models," Discussion Papers DP 2010-08, Philippine Institute for Development Studies.
    4. David Brasington & Don Haurin, 2005. "Capitalization of Parent, School, and Peer Group Components of School Quality into House Price," Departmental Working Papers 2005-04, Department of Economics, Louisiana State University.
    5. David J. Eckman & Shane G. Henderson & Sara Shashaani, 2023. "Diagnostic Tools for Evaluating and Comparing Simulation-Optimization Algorithms," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 350-367, March.
    6. Brian Irwin & Eldad Haber, 2023. "Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition," Computational Optimization and Applications, Springer, vol. 84(3), pages 651-702, April.
    7. Matteo Lapucci & Alessio Sortino, 2024. "On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties," SN Operations Research Forum, Springer, vol. 5(2), pages 1-11, June.
    8. S. Gratton & Ph. L. Toint, 2020. "A note on solving nonlinear optimization problems in variable precision," Computational Optimization and Applications, Springer, vol. 76(3), pages 917-933, July.
    9. Hongxia Wang & Jinde Wang & Bo Huang, 2012. "Prediction for spatio-temporal models with autoregression in errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 217-244.
    10. Luisa Alamá-Sabater & Laura Márquez-Ramos & Celestino Suárez-Burguet & J. Miguel Navarro-Azorín, 2012. "Interregional Trade and Transport Connectivity. An Analysis of Spatial Dependence," Working Papers 2012/20, Economics Department, Universitat Jaume I, Castellón (Spain).
    11. Lahcen El Bourkhissi & Ion Necoara, 2025. "Complexity of linearized quadratic penalty for optimization with nonlinear equality constraints," Journal of Global Optimization, Springer, vol. 91(3), pages 483-510, March.
    12. Yutao Zheng & Bing Zheng, 2017. "Two New Dai–Liao-Type Conjugate Gradient Methods for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 502-509, November.
    13. Steven Bourassa & Eva Cantoni & Martin Hoesli, 2007. "Spatial Dependence, Housing Submarkets, and House Price Prediction," The Journal of Real Estate Finance and Economics, Springer, vol. 35(2), pages 143-160, August.
    14. Giovanni Fasano & Massimo Roma, 2016. "A novel class of approximate inverse preconditioners for large positive definite linear systems in optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 399-429, November.
    15. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    16. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    17. Raja Chakir & Olivier Parent, 2009. "Determinants of land use changes: A spatial multinomial probit approach," Papers in Regional Science, Wiley Blackwell, vol. 88(2), pages 327-344, June.
    18. Brasington, David M. & Haurin, Donald R., 2009. "Parents, peers, or school inputs: Which components of school outcomes are capitalized into house value?," Regional Science and Urban Economics, Elsevier, vol. 39(5), pages 523-529, September.
    19. Yonggang Pei & Shaofang Song & Detong Zhu, 2023. "A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization," Computational Optimization and Applications, Springer, vol. 84(3), pages 1005-1033, April.
    20. Alexandre Xavier Ywata Carvalho & Pedro Henrique Melo Albuquerque & Gilberto Rezende de Almeida Junior & Rafael Dantas Guimarães, 2009. "Clusterização Hierárquica Espacial," Discussion Papers 1427, Instituto de Pesquisa Econômica Aplicada - IPEA.

    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:spr:coopap:v:91:y:2025:i:1:d:10.1007_s10589-025-00665-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.