Inheritance diagram for NOX::LineSearch::NonlinearCG:
Public Member Functions
|NonlinearCG (const Teuchos::RefCountPtr< NOX::GlobalData > &gd, Teuchos::ParameterList ¶ms)|
|bool||reset (const Teuchos::RefCountPtr< NOX::GlobalData > &gd, Teuchos::ParameterList ¶ms)|
|Reset parameters. |
|bool||compute (NOX::Abstract::Group &newgrp, double &step, const NOX::Abstract::Vector &dir, const NOX::Solver::Generic &s)|
|Perform a line search. |
This is a simple linesearch intended to be used with NOX::Direction::NonlinearCG, which provides search direction , in computing an update to the current solution vector . It is designed to compute a step length consistent with the exact linesearch of Linear CG for linear problems, and it avoids use of matrices by employing a directional derivative (details below). The step length, is computed from a single evaluation of,
where is the n x n Jacobian matrix. Explicit construction of is avoided by performing the product using a directional derivative (cf NOX::Epetra::MatrixFree):
Derivation / Theory:
This linesearch is derived by attempting to achieve in a single step, the following minimization:
where is a merit function chosen (but never explicitly given) so that an equivalence to Linear CG holds, ie . The minimization above can now be cast as an equation:
An approximate solution to this equation can be obtained from a second-order expansion of
from which it immediately follows
The NonlinearCG linesearch is selected using:
"Method" = "%NonlinearCG" [required]
Currently, no adjustable parameters exist for this linesarch.
Jonathan Richard Shewchuk, <A HREF="http://www-2.cs.cmu.edu/~jrs/jrspapers.html"/> "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain," 1994. Though presented within the context of nonlinear optimization, the connection to solving nonlinear equation systems is made via the equivalence .
Perform a line search.
In the end, we should have computed and updated