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NOX::Solver::InexactTrustRegionBased Class Reference

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

#include <NOX_Solver_InexactTrustRegionBased.H>

Inheritance diagram for NOX::Solver::InexactTrustRegionBased:
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Collaboration diagram for NOX::Solver::InexactTrustRegionBased:
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List of all members.

Public Member Functions

 InexactTrustRegionBased (const Teuchos::RCP< NOX::Abstract::Group > &grp, const Teuchos::RCP< NOX::StatusTest::Generic > &tests, const Teuchos::RCP< Teuchos::ParameterList > &params)
virtual ~InexactTrustRegionBased ()
virtual void reset (const NOX::Abstract::Vector &initialGuess, const Teuchos::RCP< NOX::StatusTest::Generic > &tests)
 Resets the solver, sets a new status test, and sets a new initial guess.
virtual void reset (const NOX::Abstract::Vector &initialGuess)
 Resets the solver and sets a new initial guess.
virtual NOX::StatusTest::StatusType getStatus ()
 Check current convergence and failure status.
virtual NOX::StatusTest::StatusType step ()
 Do one nonlinear step in the iteration sequence and return status.
virtual NOX::StatusTest::StatusType solve ()
 Solve the nonlinear problem and return final status.
virtual const
getSolutionGroup () const
 Return a reference to the current solution group.
virtual const
getPreviousSolutionGroup () const
 Return a reference to the previous solution group.
virtual int getNumIterations () const
 Get number of iterations.
virtual const
getList () const
 Return a reference to the solver parameters.
virtual Teuchos::RCP< const
getSolutionGroupPtr () const
 Return a RCP to the solution group.
virtual Teuchos::RCP< const
getPreviousSolutionGroupPtr () const
 Return a RCP to the previous solution group.
virtual Teuchos::RCP< const
getListPtr () const
 Return a RCP to the solver parameters.

Protected Types

enum  TrustRegionType { Standard, Inexact }
 Type of Trust Region algorithm to use. More...
enum  InnerIterationReturnType { Converged, Unconverged, Failed }
 Return types for inner iteration status test. More...
enum  StepType { Newton, Cauchy, Dogleg }
 Enumerated list for each direction that may be required in the Trust region computation. More...

Protected Member Functions

virtual NOX::StatusTest::StatusType iterateStandard ()
 "Standard" trust region implementation
virtual NOX::StatusTest::StatusType iterateInexact ()
 "Inexact Trust Region"
virtual void init ()
 Print out initialization information and calcuation the RHS.
virtual void printUpdate ()
 Prints the current iteration information.
virtual void invalid (const std::string &param, double value) const
 Print an error message and throw an error during parameter reads.
virtual void throwError (const std::string &method, const std::string &mesage) const
 Print an error message and throw an error.
virtual void resetCounters ()
 Resets the counters in the solver.
NOX::StatusTest::StatusType checkStep (const NOX::Abstract::Vector &step, double &radius)
 Check to see if the current step is acceptable. If not, it reduces the trust region radius accordingly.
virtual double computeNorm (const NOX::Abstract::Vector &v)
 Computes the norm of a given vector.

Protected Attributes

TrustRegionType method
 Type of trust region algorithm to use.
Teuchos::RCP< NOX::GlobalDataglobalDataPtr
 Pointer to the global data object.
Teuchos::RCP< NOX::Utilsutils
InnerIterationReturnType innerIterationStatus
 Current status of the trust region inner iteration.
< NOX::Abstract::Group
 Current solution.
< NOX::Abstract::Group
 Previous solution pointer.
< NOX::Abstract::Vector
 Current newton direction pointer.
< NOX::Abstract::Vector
 Current cauchy direction pointer.
< NOX::Abstract::Vector
 Extra vector used in computations.
< NOX::Abstract::Vector
 Extra vector used in computations.
< NOX::Abstract::Vector
 Extra vector used in computations.
< NOX::Abstract::Vector
 Extra vector used in computations.
< NOX::StatusTest::Generic
 Stopping test.
< Teuchos::ParameterList
 Input parameters.
NOX::Direction::Utils::InexactNewton inNewtonUtils
 Inexact Newton utitilities.
< NOX::Direction::Generic
 Newton Search Direction.
< NOX::Direction::Generic
 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.
double eta
 Current linear solve tolerance (inexact only).
double eta_last
 Linear solve tolerance used in last iteration (inexact only).
NOX::StatusTest::StatusType status
 Status of nonlinear solver.
NOX::StatusTest::CheckType checkType
 Type of check to use for status tests. See NOX::StatusTest for more details.
StepType stepType
 Type of step to be taken.
< NOX::MeritFunction::Generic
 Stores merit function supplied by global data.
bool useCauchyInNewtonDirection
 If set to true, the initial guess for the Newton direction computation will use the Cauchy direction as the initial guess.
bool writeOutputParamsToList
 If set to true, statistics/counters will be output to the output list.
bool useCounters
 If set to true, counters will be stored by the solver.
int numCauchySteps
 Counter for the number of cauchy steps taken.
int numNewtonSteps
 Counter for the number of Newton steps taken.
int numDoglegSteps
 Counter for the number of Dogleg steps taken.
int numTrustRegionInnerIterations
 Number of inner iterations required to adjust the trust region radius.
double sumDoglegFracCauchyToNewton
 Hold the sum of the value of the fraction a dogleg step took between the Cauchy and Newton directions. This is the $ \gamma $ variable in the standard dogleg algorithm and the $ \tau $ parameter in the inexact dogleg algorithm. A value of 0.0 is a full step in the Cauchy direction and a value of 1.0 is a full step in the Newton direction.
double sumDoglegFracNewtonLength
 Holds the sum of the values of the fraction a dogleg step took compared to the full Newton step. The fractional value is computed as $ \mbox{frac} = \frac{\| d \|}{\| n\|} $.
bool useAredPredRatio
 If set to true, the minimum improvement ratio condition uses an Ared/Pred approach.
bool useDoglegMinimization
 If set to true, the $ \tau $ parameter is minimized over the dogleg line segments instead of being computed at the trust regioin radius.
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)} $


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 called "Output" will be created at the top level of the parameter list and contain the following general solver parameters:

A sublist called "Output" will be created in the "Trust Region" sublist and contain the following trust region specific output parameters:

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

Member Enumeration Documentation

Return types for inner iteration status test.






Failed by hitting minimum radius bound.

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


Use the Newton direction.


Use the Cauchy direction.


Use the doglog direction.

Type of Trust Region algorithm to use.


Basic trust region method for nonlinear systems (Nocedal and Wright?).


Inexact Trust region WITHOUT minimization of the local linear model over the line segments.

Constructor & Destructor Documentation

NOX::Solver::InexactTrustRegionBased::InexactTrustRegionBased ( const Teuchos::RCP< NOX::Abstract::Group > &  grp,
const Teuchos::RCP< NOX::StatusTest::Generic > &  tests,
const Teuchos::RCP< Teuchos::ParameterList > &  params 


See reset() for description.

References init(), and rcp().

Member Function Documentation

double NOX::Solver::InexactTrustRegionBased::computeNorm ( const NOX::Abstract::Vector v) [protected, virtual]

Computes the norm of a given vector.

Defaults to the L-2 norm but could use a user defined norm also.

References NOX::Abstract::Vector::norm().

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::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.

References Teuchos::ParameterList::set(), Teuchos::ParameterList::sublist(), and NOX::StatusTest::Unconverged.

Member Data Documentation

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:
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