NOX::Direction::NonlinearCG Class Reference

Calculates a search direction using the Nonlinear Conjugate Gradient method. More...

#include <NOX_Direction_NonlinearCG.H>

Inheritance diagram for NOX::Direction::NonlinearCG:

Inheritance graph
[legend]
Collaboration diagram for NOX::Direction::NonlinearCG:

Collaboration graph
[legend]
List of all members.

Public Member Functions

 NonlinearCG (const Teuchos::RCP< NOX::GlobalData > &gd, Teuchos::ParameterList &params)
 Constructor.
virtual ~NonlinearCG ()
 Destructor.
virtual bool reset (const Teuchos::RCP< NOX::GlobalData > &gd, Teuchos::ParameterList &p)
 derived
virtual bool compute (Abstract::Vector &dir, Abstract::Group &grp, const Solver::Generic &solver)
 derived
virtual bool compute (NOX::Abstract::Vector &dir, NOX::Abstract::Group &grp, const NOX::Solver::LineSearchBased &solver)
 Same as compute(NOX::Abstract::Vector&, NOX::Abstract::Group&, const NOX::Solver::Generic&).

Detailed Description

Calculates a search direction using the Nonlinear Conjugate Gradient method.

Calculates the direction

\[ d = - M^{-1}(x) F(x) + \beta d_{prev} \]

where $ M $ is a preconditioner and $ \beta $ is an orthogonalization parameter which can be computed in various ways (see below), and $ d_{prev} $ is the search direction from the previous nonlinear iteration.

This method provides a generalization of Linear CG to nonlinear problems. It does this by computing a search direction using an expression analogous to that of Linear CG. The negative of the current residual vector, $ F(x) $ is taken, allowed to be preconditioned, and then orthogonalized against the previous search direction. This direction can sometimes be used successfully with the various choices provided in NOX::Linesearch but is intended to be used with NOX::Linesearch::NonlinearCG. In fact, the expected convergence behavior of linear problems can only be achieved in this way.

To use this direction, specify that the "Method" is "NonlinearCG" 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).

The following options may be specified in the "Nonlinear CG" sublist of the "Direction" sublist of the solver parameters.

References

information about both linear and nonlinear conjugate gradient methods can be found in Chapter 5 of:

Nocedal & Wright, "Numerical Optimization", Springer-Verlag, New York, 1999. Though presented within the context of nonlinear optimization, the connection to nonlinear systems of equations is made by the correspondence $ \nabla f(x) \leftrightarrow F(x) $ (cf Algorithm 5.4).

Another useful useful reference is:

Jonathan Richard Shewchuk, "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain," 1994. Chapter 14 provides a summary of issues in generalizing linear CG to the nonlinear case. Correspondence to NOX notation is made by the equivalence $ r \leftrightarrow f' \leftrightarrow F(x) $ (cd Section 14.1).


Member Function Documentation

bool NonlinearCG::compute ( NOX::Abstract::Vector dir,
NOX::Abstract::Group grp,
const NOX::Solver::LineSearchBased solver 
) [virtual]

Same as compute(NOX::Abstract::Vector&, NOX::Abstract::Group&, const NOX::Solver::Generic&).

Enables direct support for line search based solvers for the purpose of efficiency since the LineSearchBased object has a getStep() function that some directions require.

If it is not redefined in the derived class, it will just call the compute with the NOX::Solver::Generic argument.

Reimplemented from NOX::Direction::Generic.


The documentation for this class was generated from the following files:
Generated on Wed May 12 21:41:59 2010 for NOX by  doxygen 1.4.7