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

Algorithm 12.2: Dogleg method to find an approximation of the trust region subproblem. More...

Go to the source code of this file.

Functions

function dogleg (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 Dogleg method to find an approximate solution. More...

 

Detailed Description

Algorithm 12.2: Dogleg method to find an approximation of the trust region subproblem.

Implementation of algorithm 12.2 of [1]

Author
Michel Bierlaire
Date
Sat Mar 21 15:43:44 2015

Definition in file dogleg.m.

Function Documentation

function dogleg ( 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 Dogleg method to find an approximate solution.

Note
Tested with run1203dogleg.m
Calls intersectionTrustRegion
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 -2: negative curvature along Newton's direction
  • type -1: negative curvature along Cauchy's direction (i.e. along the gradient)
  • type 1: Partial Cauchy step
  • type 2: Newton step
  • type 3: Partial Newton step
  • type 4: Dogleg
Copyright 2015-2016 Michel Bierlaire