Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould; M. Porcelli; Philippe Toint

doi:10.1007/s10589-011-9446-7

Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould, M. Porcelli, Philippe Toint

Research output: Contribution to journal › Article › peer-review

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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. © 2011 Springer Science+Business Media, LLC.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Computational Optimization and Applications
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s10589-011-9446-7
Publication status	Published - 1 Sept 2012

Keywords

numerical performance
unconstrained optimization
cubic regularization

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10.1007/s10589-011-9446-7

71534Submitted manuscript, 518 KB

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Updating the regularization parameter in the adaptive cubic regularization algorithm

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Evaluation complexity of algorithms for nonconvex optimization

Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Polytechnic University of Hong Kong

University of Oxford

Cite this

Updating the regularization parameter in the adaptive cubic regularization algorithm

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Research output

Evaluation complexity of algorithms for nonconvex optimization

Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization

Projects

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Activities

Polytechnic University of Hong Kong

University of Oxford

Cite this