Optimization Online


Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould (nick.gould***at***sftc.ac.uk)
Margherita Porcelli (porcelli***at***math.unifi.it)
Philippe Toint (philippe.toint***at***fundp.ac.be)

Abstract: The adaptive cubic regularization method [Cartis, Gould, Toint, 2009-2010] 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.

Keywords: unconstrained optimization, cubic regularization, numerical performance

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: N. I. M. Gould, M. Porcelli and Ph. L. Toint, "Updating the regularization parameter in the adaptive cubic regularization algorithm", Computational Optimization and Applications, 53:1 (2012), pp. 1-22. DOI: 10.1007/s10589-011-9446-7.

Download: [PDF]

Entry Submitted: 02/24/2011
Entry Accepted: 02/24/2011
Entry Last Modified: 11/09/2013

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society