newtonTrustRegion.m File Reference

Algorithm 12.4: Newton's method with trust region. More...

Go to the source code of this file.

Functions
function	newtonTrustRegion (in obj, in x0, in delta0, in eps, in tr)
	Applies Newton's algorithm with trust region to solve where . The parameters of the method are taken from [2] (p. 117). More...

Detailed Description

Algorithm 12.4: Newton's method with trust region.

Implementation of algorithm 12.4 of [1]

Author

Michel Bierlaire

Date

Sat Mar 21 16:04:27 2015

Definition in file newtonTrustRegion.m.

Function Documentation

newtonTrustRegion()

function newtonTrustRegion	(	in	obj,
		in	x0,
		in	delta0,
		in	eps,
		in	tr
	)

Applies Newton's algorithm with trust region to solve where . The parameters of the method are taken from [2] (p. 117).

Note

Tested with run0508tr.m

Tested with runRosenbrockTrustRegion.m

Calls dogleg

Calls truncatedConjugateGradient

Parameters

obj	the name of the Octave function defining f(x) and its derivatives
x0	the starting point
delta0	radius of the initial trust region
eps	algorithm stops if .
tr	method to solve the trust region subproblem. If 0, the dogleg method is used. If different from 0, the truncated conjugate gradient is used (default: 0).
maxiter	maximum number of iterations (Default: 100)

Returns

[solution,iteres,niter]

solution: local minimum of the function

iteres: sequence of iterates generated by the algorithm. It contains n+2 columns. Columns 1:n contains the value of the current iterate. Column n+1 contains the value of the objective function. Column n+2 contains the value of the norm of the gradient. It contains maxiter rows, but only the first niter rows are meaningful.

niter: total number of iterations