NOX::Direction::Broyden Class Reference

Broyden direction More...

#include <NOX_Direction_Broyden.H>

Inheritance diagram for NOX::Direction::Broyden:

[legend]Collaboration diagram for NOX::Direction::Broyden:[legend]List of all members.


Public Member Functions
	Broyden (const Teuchos::RefCountPtr< NOX::GlobalData > &gd, Teuchos::ParameterList &params)
	Constructor.
virtual	~Broyden ()
	Destructor.
virtual bool	reset (const Teuchos::RefCountPtr< NOX::GlobalData > &gd, Teuchos::ParameterList &params)
	Reset direction based on possibly new parameters.
virtual bool	compute (NOX::Abstract::Vector &dir, NOX::Abstract::Group &grp, const NOX::Solver::Generic &solver)
	Not supported for this direction - only works for line search based solver.
virtual bool	compute (NOX::Abstract::Vector &dir, NOX::Abstract::Group &grp, const NOX::Solver::LineSearchBased &solver)

Detailed Description

Broyden direction

We will calculate a limited-memory Broyden direction of the form

$d_k = -B_k^{-1} F_k.$

Here $B_k$ is a limited-memory Broyden approximation to the Jacobian of $F$ at $x_k$ , and $F_k = F(x_k)$ . It is based on apply Broyden updates to the Jacobian from some previous step.

Note:: The Broyden direction can only be used with NOX::Solver::LineSearchBased. It cannot be used with any other solver, include NOX::Solver::TrustRegionBased.

References

C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995.

Parameters

To use this direction, specify that the "Method" is "Broyden" in the "Direction" sublist of the parameters that are passed to the solver (see NOX::Direction::Manager for more information on choosing the search direction).

In "Direction"/"Broyden":

"Restart Frequency" - How often the Jacobian should be refreshed. A value of 5, for example, means that the Jacobian should be updated every 5 iterations. Defaults to 10.
"Max Convergence Rate" - Maximum convergence rate allowed when reusing the Jacobian. The Jacobian will be refreshed if the convergence rate, $\alpha$ , is larger than this value. The convergence rate is calculated by $\alpha = \frac{\| F_k \| }{\| F_{k-1} \|}$ where F is the nonlinear residual and is the nonlinear iteration. Defaults to 1.0.
"Memory" - The maximum number of past updates that can be saved in memory. Defaults to the value of "Restart Frequency".
"Linear Solver" - optional SUBLIST of linear solver parameters.
"Linear Solver"/"Tolerance" - Desired tolerance for linear solve. Defaults to 1.0e-4. The tolerance can be computed using adaptive forcing terms. See NOX::Direction::Utils::InexactNewton for additional options.

Member Function Documentation

bool NOX::Direction::Broyden::compute ( NOX::Abstract::Vector & dir,

NOX::Abstract::Group & soln,

const NOX::Solver::LineSearchBased & solver

) [virtual]

Add this direction to the memory
Reimplemented from NOX::Direction::Generic.

The documentation for this class was generated from the following files:

NOX_Direction_Broyden.H
NOX_Direction_Broyden.C

Generated on Thu Sep 18 12:38:37 2008 for NOX by

1.3.9.1

NOX::Direction::Broyden Class Reference

Public Member Functions

Detailed Description

Member Function Documentation