IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v53y2012i1p1-22.html
   My bibliography  Save this article

Updating the regularization parameter in the adaptive cubic regularization algorithm

Author

Listed:
  • N. Gould
  • M. Porcelli
  • P. Toint

Abstract

The adaptive cubic regularization method (Cartis et al. in Math. Program. Ser. A 127(2):245–295, 2011 ; Math. Program. Ser. A. 130(2):295–319, 2011 ) has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to the local Lipschitz constant of the objective’s Hessian. We present new updating strategies for this parameter based on interpolation techniques, which improve the overall numerical performance of the algorithm. Numerical experiments on large nonlinear least-squares problems are provided. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • N. Gould & M. Porcelli & P. Toint, 2012. "Updating the regularization parameter in the adaptive cubic regularization algorithm," Computational Optimization and Applications, Springer, vol. 53(1), pages 1-22, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:1-22
    DOI: 10.1007/s10589-011-9446-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-011-9446-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-011-9446-7?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. Elias L. Khalil (ed.), 2003. "Trust," Books, Edward Elgar Publishing, number 2482.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hande Benson & David Shanno, 2014. "Interior-point methods for nonconvex nonlinear programming: cubic regularization," Computational Optimization and Applications, Springer, vol. 58(2), pages 323-346, June.
    2. E. G. Birgin & J. M. Martínez, 2019. "A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization," Computational Optimization and Applications, Springer, vol. 73(3), pages 707-753, July.
    3. J. M. Martínez & M. Raydan, 2017. "Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization," Journal of Global Optimization, Springer, vol. 68(2), pages 367-385, June.
    4. Tommaso Bianconcini & Giampaolo Liuzzi & Benedetta Morini & Marco Sciandrone, 2015. "On the use of iterative methods in cubic regularization for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 60(1), pages 35-57, January.
    5. 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.
    6. J. Martínez & M. Raydan, 2015. "Separable cubic modeling and a trust-region strategy for unconstrained minimization with impact in global optimization," Journal of Global Optimization, Springer, vol. 63(2), pages 319-342, October.
    7. Elizabeth Karas & Sandra Santos & Benar Svaiter, 2015. "Algebraic rules for quadratic regularization of Newton’s method," Computational Optimization and Applications, Springer, vol. 60(2), pages 343-376, March.

    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. Buccirossi, Paolo & Spagnolo, Giancarlo, 2006. "Leniency policies and illegal transactions," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1281-1297, August.
    2. Chakravarty, Sugato & Jain, Pankaj & Upson, James & Wood, Robert, 2012. "Clean Sweep: Informed Trading through Intermarket Sweep Orders," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(2), pages 415-435, April.
    3. Alberto Alesina & Edward Glaeser & Bruce Sacerdote, 2001. "Why Doesn't The US Have a European-Style Welfare State?," Harvard Institute of Economic Research Working Papers 1933, Harvard - Institute of Economic Research.
    4. Neven, Damien J. & Roller, Lars-Hendrik, 2000. "The allocation of jurisdiction in international antitrust," European Economic Review, Elsevier, vol. 44(4-6), pages 845-855, May.
    5. Arturo Vásquez & Raúl García & Edwin Quintanilla & Julio Salvador & David Orosco, 2012. "Acceso a la Energía en el Perú : Algunas Opciones de Política," Working Papers 29, Osinergmin, Gerencia de Políticas y Análisis Económico.
    6. William Shughart & Fred McChesney, 2010. "Public choice theory and antitrust policy," Public Choice, Springer, vol. 142(3), pages 385-406, March.
    7. Bernard Reddy & David Evans & Albert Nichols & Richard Schmalensee, 2001. "A Monopolist Would Still Charge More for Windows: A Comment on Werden," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 18(3), pages 263-268, May.
    8. Evenett, Simon J., 2003. "Do all networks facilitate international commerce? US law firms and the international market for corporate control," Journal of the Japanese and International Economies, Elsevier, vol. 17(4), pages 520-537, December.
    9. Fengxia Dong & Thomas L. Marsh & Kyle W. Stiegert, 2006. "State Trading Enterprises in a Differentiated Product Environment: The Case of Global Malting Barley Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(1), pages 90-103.
    10. Bastin, Fabian & Cirillo, Cinzia & Toint, Philippe L., 2006. "Application of an adaptive Monte Carlo algorithm to mixed logit estimation," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 577-593, August.
    11. van der Loos, Matthijs J. H. M. & Benjamin, Daniel J. & Cesarini, David & Dawes, Christopher T. & Koellinger, Philipp D. & Magnusson, Patrik K. E. & Chabris, Christopher F. & Conley, Dalton & Laibson,, 2012. "The Genetic Architecture of Economic and Political Preferences," Scholarly Articles 10121961, Harvard University Department of Economics.
    12. Edward L. Glaeser & Bruce I. Sacerdote, 2008. "Education and Religion," Journal of Human Capital, University of Chicago Press, vol. 2(2), pages 188-215.
    13. Philip Gayle & Dennis Weisman, 2007. "Are input prices irrelevant for make-or-buy decisions?," Journal of Regulatory Economics, Springer, vol. 32(2), pages 195-207, October.
    14. Alberto Alesina & Edward Glaeser & Bruce Sacerdote, 2001. "Why Doesn't the US Have a European-Style Welfare System?," NBER Working Papers 8524, National Bureau of Economic Research, Inc.
    15. Bigoni, Maria & Fridolfsson, Sven-Olof & Le Coq, Chloé & Spagnolo, Giancarlo, 2008. "Fines, Leniency and Rewards in Antitrust: An Experiment," Working Paper Series 738, Research Institute of Industrial Economics, revised 06 Aug 2009.
    16. Edward L. Glaeser & David Laibson & Bruce Sacerdote, 2002. "An Economic Approach to Social Capital," Economic Journal, Royal Economic Society, vol. 112(483), pages 437-458, November.
    17. Serge Gratton & Selime Gürol & Philippe Toint, 2013. "Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems," Computational Optimization and Applications, Springer, vol. 54(1), pages 1-25, January.

    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:53:y:2012:i:1:p:1-22. 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.