Updating the regularization parameter in the adaptive 
                    cubic regularization algorithm

              N. I. M. Gould, M. Porcelli and Ph. L. Toint

                Report naXys-08-2011  10 February 2011

Abstract.   The  adaptive  cubic  regularization  method  (Cartis,  Gould  and
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.