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

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

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
gthe gradient $ \nabla f(\widehat{x})$
Hthe hessian $ \nabla^2 f(\widehat{x})$
deltathe 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 2015-2016 Michel Bierlaire