The extended Newton-Raphson minimization scheme ROBMIN

 

        Define the functions

Equation 1

and

Equation 2

 

The l is a generalization of the Marquardt prameter discussed by Press under the heading “Levenberg-Marquardt Method” in section 15.5 of  the 1992 editionsection 14.4 of the 1986 edition.   The Si's are relative smoothers which measure the relative non-linearity of the various parameters. 

        The constants which minimize equation 2 are.  These can be inserted into equation 1 to find .  Then the lambda can be found for which .