Optimization: principles and algorithms, by Michel Bierlaire: chap12/truncatedConjugateGradient.m File Reference

Optimization: principles and algorithms, by Michel Bierlaire

chap12

Algorithm 12.3: Truncated conjugate gradients method to find an approximation of the trust region subproblem. More...

Go to the source code of this file.

Functions
function	truncatedConjugateGradient (in g, in H, in delta)
	Given a current iterate $\widehat{x}$ , consider the trust region subproblem $\min_d d^T \nabla f(\widehat{x}) + \frac{1}{2} d^T \nabla^2 f(\widehat{x}) d$ subject to $\\|d\\|_2 \leq \Delta.$ Apply the truncated conjugate gradients method to find an approximate solution. More...

Detailed Description

Algorithm 12.3: Truncated conjugate gradients method to find an approximation of the trust region subproblem.

Implementation of algorithm 12.3 of [1]

Author: Michel Bierlaire

Date: Sat Mar 21 15:49:09 2015

Definition in file truncatedConjugateGradient.m.

Function Documentation

◆ truncatedConjugateGradient()

function truncatedConjugateGradient	(	in	g,
		in	H,
		in	delta
	)

Given a current iterate $\widehat{x}$ , consider the trust region subproblem

$\min_d d^T \nabla f(\widehat{x}) + \frac{1}{2} d^T \nabla^2 f(\widehat{x}) d$

subject to

$\|d\|_2 \leq \Delta.$

Apply the truncated conjugate gradients method to find an approximate solution.

Note: Tested with run1203tcg.m; Called by newtonTrustRegion; Called by symmetricRankOne

Parameters

g	the gradient $\nabla f(\widehat{x})$
H	the hessian $\nabla^2 f(\widehat{x})$
delta	the radius $\Delta$ of the trust region

Returns

[dstar,type]

dstar: the approximate solution

type: the type of outcome of the method, based on the following code:

type 1: convergence
type 2: out of the trust region
type 3: negative curvature detected

Copyright 2015-2018 Michel Bierlaire