Optimization: principles and algorithms, by Michel Bierlaire
Functions
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 $\min_x f(x)$ where $f:\mathbb{R}^n\to\mathbb{R}$. 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

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

Applies Newton's algorithm with trust region to solve $\min_x f(x)$ where $f:\mathbb{R}^n\to\mathbb{R}$. 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
objthe name of the Octave function defining f(x) and its derivatives
x0the starting point
delta0radius of the initial trust region
epsalgorithm stops if $\|F(x)\| \leq \varepsilon $.
trmethod 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).
maxitermaximum 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
Copyright 2015-2016 Michel Bierlaire