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  , consider the trust region subproblem
subject to
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]
- Date
- Sat Mar 21 15:43:44 2015
Definition in file dogleg.m.
Function Documentation
◆ dogleg()
| function dogleg | ( | in | g, |
| in | H, | ||
| in | delta | ||
| ) |
Given a current iterate , consider the trust region subproblem
![\[ \min_d d^T \nabla f(\widehat{x}) + \frac{1}{2} d^T \nabla^2 f(\widehat{x}) d \]](form_48.png)
subject to
![\[\|d\|_2 \leq \Delta. \]](form_49.png)
Apply the Dogleg method to find an approximate solution.
- Note
- Tested with run1203dogleg.m
- Calls intersectionTrustRegion
- Called by newtonTrustRegion
- Called by symmetricRankOne
- Parameters
-
g the gradient 
H the hessian 
delta the radius 
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