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Updating the regularization parameter in the adaptive cubic regularization algorithm

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  • 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
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    1. Elias L. Khalil (ed.), 2003. "Trust," Books, Edward Elgar Publishing, number 2482.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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