NOX::Solver::TrustRegionBased Class Reference

Newton-like solver using a trust region. More...

#include <NOX_Solver_TrustRegionBased.H>

Inheritance diagram for NOX::Solver::TrustRegionBased:

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Collaboration diagram for NOX::Solver::TrustRegionBased:
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List of all members.

Public Member Functions

 TrustRegionBased (NOX::Abstract::Group &xgrp, NOX::StatusTest::Generic &t, NOX::Parameter::List &p)
 Constructor.
virtual ~TrustRegionBased ()
 Destructor.
virtual bool reset (NOX::Abstract::Group &xgrp, NOX::StatusTest::Generic &t, NOX::Parameter::List &p)
 Reset the nonlinear solver for a new solve.
virtual bool reset (NOX::Abstract::Group &xgrp, NOX::StatusTest::Generic &t)
 A soft reset of the nonlinear solver for a new problem.
virtual NOX::StatusTest::StatusType getStatus ()
 Check current convergence and failure status.
virtual NOX::StatusTest::StatusType iterate ()
 Do one nonlinear method iteration and return status.
virtual NOX::StatusTest::StatusType solve ()
 Solve the nonlinear problem and return final status.
virtual const NOX::Abstract::GroupgetSolutionGroup () const
 Return a reference to the current solution group.
virtual const NOX::Abstract::GroupgetPreviousSolutionGroup () const
 Return a reference to the previous solution group.
virtual int getNumIterations () const
 Get number of iterations.
virtual const NOX::Parameter::ListgetParameterList () const
 Return a refernece to the solver parameters.

Protected Types

enum  StepType { Newton, Cauchy, Dogleg }
 Enumerated list for each direction that may be required in the Trust region computation. More...

Protected Member Functions

virtual void init ()
 Print out initialization information and calcuation the RHS.
virtual void invalid (const string &param, double value) const
 Print and error message and throw and error.
virtual void printUpdate ()
 Prints the current iteration information.

Protected Attributes

NOX::Abstract::GroupsolnPtr
 Current solution.
NOX::Abstract::GroupoldSolnPtr
 Previous solution pointer.
NOX::Abstract::GroupoldSoln
 Previous solution reference.
NOX::Abstract::VectornewtonVecPtr
 Current search direction.pointer.
NOX::Abstract::VectornewtonVec
 Current Newton direction.reference.
NOX::Abstract::VectorcauchyVecPtr
 Current search direction.pointer.
NOX::Abstract::VectorcauchyVec
 Current Cauchy direction.reference.
NOX::Abstract::VectoraVecPtr
 Extra vector used in computations.
NOX::Abstract::VectoraVec
 Extra vector.
NOX::Abstract::VectorbVecPtr
 Extra vector used in computations.
NOX::Abstract::VectorbVec
 Extra vector.
NOX::StatusTest::GenerictestPtr
 Stopping test.
NOX::Parameter::ListparamsPtr
 Input parameters.
NOX::Utils utils
 Printing Utils.
NOX::Direction::Manager newton
 Newton Search Direction.
NOX::Direction::Manager cauchy
 Cauchy Search Direction.
double radius
 Radius of the trust region.
double minRatio
 Minimum improvement ratio to accept step.
double minRadius
 Minimum trust region radius.
double maxRadius
 Maximum trust region radius.
double contractTriggerRatio
 ratio < alpha triggers contraction
double expandTriggerRatio
 ratio > beta triggers expansion
double expandFactor
 Expansion factor.
double contractFactor
 Constraction factor.
double recoveryStep
double newF
 Value of $ f $ at current solution.
double oldF
 Value of $ f $ at previous solution.
double dx
 norm(xnew - xold)
int nIter
 Number of nonlinear iterations.
NOX::StatusTest::StatusType status
 Status of nonlinear solver.
StepType stepType
 Type of step to be taken.
NOX::Parameter::UserNormuserNormPtr
 Stores a user supplied norm if supplied in the parameter list.
NOX::Parameter::MeritFunctionuserMeritFuncPtr
 Stores a user supplied merit function if supplied in the parameter list.
bool useAredPredRatio
 If set to true, the minimum improvement ratio condition uses an Ared/Pred approach.
NOX::Solver::PrePostOperator prePostOperator
 Pointer to a user defined NOX::Abstract::PrePostOperator object.

Detailed Description

Newton-like solver using a trust region.

Our goal is to solve: $ F(x) = 0, $ where $ F:\Re^n \rightarrow \Re^n $. Alternatively, we might say that we wish to solve

   $ \min f(x) \equiv \frac{1}{2} \|F(x)\|^2_2. $

The trust region subproblem (TRSP) at iteration $k$ is given by

   $ \min \; m_k(s) \equiv f_k + g_k^T d + \frac{1}{2} d^T B_k d, \mbox{ s.t. } \|d\| \leq \Delta_k \quad \mbox{(TRSP)} $

where

The "improvement ratio" for a given step $ s $ is defined as

   $ \rho = \displaystyle\frac{ f(x_k) - f(x_k + d) } { m_k(0) - m_k(d) } $

An iteration consists of the following steps.

Input Paramters

The following parameters should be specified in the "Trust Region" sublist based to the solver.

Output Paramters

A sublist for output parameters called "Output" will be created and contain the following parameters:

Author:
Tammy Kolda (SNL 8950), Roger Pawlowski (SNL 9233)


Member Enumeration Documentation

enum NOX::Solver::TrustRegionBased::StepType [protected]
 

Enumerated list for each direction that may be required in the Trust region computation.

Enumeration values:
Newton  Use the Newton direction.
Cauchy  Use the Cauchy direction.
Dogleg  Use the doglog direction.


Constructor & Destructor Documentation

TrustRegionBased::TrustRegionBased NOX::Abstract::Group xgrp,
NOX::StatusTest::Generic t,
NOX::Parameter::List p
 

Constructor.

See reset() for description.


Member Function Documentation

bool TrustRegionBased::reset NOX::Abstract::Group xgrp,
NOX::StatusTest::Generic t
[virtual]
 

A soft reset of the nonlinear solver for a new problem.

This is a light-weight version of reset that takes no parameter list. Therefore, this reset only resets counters, the initial guess (contained in the grp argument) and new status tests (contained in the tests argument).

This reset allows problems to bypass the potentially time consuming parsing of the parameter lists.

Implements NOX::Solver::Generic.

bool TrustRegionBased::reset NOX::Abstract::Group xgrp,
NOX::StatusTest::Generic t,
NOX::Parameter::List p
[virtual]
 

Reset the nonlinear solver for a new solve.

Parameters:
grp On input, contains the intial guess. On output, contains the solution.
tests Status tests to check for convergence or failure. These tests will be modified by the solver.
params List of parameters. These parameters will be modified by the solver.
Note:
All the objects passed to reset() will be modified.

The group object will be cloned via NOX::Abstract::Group::clone(), and the vectors within will also be individually cloned via NOX::Abstract::Vector::clone().

Warning:
If the contents of grp, tests, or params are modified by the calling program after calling reset(), then the behavior of iterate() and solve() are completely undefined. To remedy this, call reset() again with the modified objects.

Implements NOX::Solver::Generic.

NOX::StatusTest::StatusType TrustRegionBased::solve  )  [virtual]
 

Solve the nonlinear problem and return final status.

By "solve", we call iterate() until the NOX::StatusTest value is either NOX::StatusTest::Converged or NOX::StatusTest::Failed.

Implements NOX::Solver::Generic.


Member Data Documentation

NOX::Abstract::Vector* NOX::Solver::TrustRegionBased::aVecPtr [protected]
 

Extra vector used in computations.

We have both a pointer and a reference because we need to create a DERIVED object and then want to have a reference to it.

NOX::Abstract::Vector* NOX::Solver::TrustRegionBased::bVecPtr [protected]
 

Extra vector used in computations.

We have both a pointer and a reference because we need to create a DERIVED object and then want to have a reference to it.

NOX::Abstract::Vector* NOX::Solver::TrustRegionBased::cauchyVecPtr [protected]
 

Current search direction.pointer.

We have both a pointer and a reference because we need to create a DERIVED object and then want to have a reference to it.

NOX::Abstract::Vector* NOX::Solver::TrustRegionBased::newtonVecPtr [protected]
 

Current search direction.pointer.

We have both a pointer and a reference because we need to create a DERIVED object and then want to have a reference to it.

NOX::Abstract::Group* NOX::Solver::TrustRegionBased::oldSolnPtr [protected]
 

Previous solution pointer.

We have both a pointer and a reference because we need to create a DERIVED object and then want to have a reference to it.

double NOX::Solver::TrustRegionBased::recoveryStep [protected]
 

Take a step of this length in the Newton direction if the trust-region search fails


The documentation for this class was generated from the following files:
Generated on Thu Sep 18 12:42:29 2008 for NOX by doxygen 1.3.9.1