NOX::Solver::InexactTrustRegionBased Class Reference

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

#include <NOX_Solver_InexactTrustRegionBased.H>

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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)
 Constructor.
virtual ~InexactTrustRegionBased ()
 Destructor.
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
NOX::Abstract::Group
getSolutionGroup () const
 Return a reference to the current solution group.
virtual const
NOX::Abstract::Group
getPreviousSolutionGroup () const
 Return a reference to the previous solution group.
virtual int getNumIterations () const
 Get number of iterations.
virtual const
Teuchos::ParameterList & 
getList () const
 Return a refernece 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 string &param, double value) const
 Print an error message and throw an error during parameter reads.
virtual void throwError (const string &method, const 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
 Utils.
InnerIterationReturnType innerIterationStatus
 Current status of the trust region inner iteration.
Teuchos::RCP
< NOX::Abstract::Group
solnPtr
 Current solution.
Teuchos::RCP
< NOX::Abstract::Group
oldSolnPtr
 Previous solution pointer.
Teuchos::RCP
< NOX::Abstract::Vector
newtonVecPtr
 Current newton direction pointer.
Teuchos::RCP
< NOX::Abstract::Vector
cauchyVecPtr
 Current cauchy direction pointer.
Teuchos::RCP
< NOX::Abstract::Vector
rCauchyVecPtr
 Extra vector used in computations.
Teuchos::RCP
< NOX::Abstract::Vector
residualVecPtr
 Extra vector used in computations.
Teuchos::RCP
< NOX::Abstract::Vector
aVecPtr
 Extra vector used in computations.
Teuchos::RCP
< NOX::Abstract::Vector
bVecPtr
 Extra vector used in computations.
Teuchos::RCP
< NOX::StatusTest::Generic
testPtr
 Stopping test.
Teuchos::RCP
< Teuchos::ParameterList > 
paramsPtr
 Input parameters.
NOX::Direction::Utils::InexactNewton inNewtonUtils
 Inexact Newton utitilities.
Teuchos::RCP
< NOX::Direction::Generic
newtonPtr
 Newton Search Direction.
Teuchos::RCP
< NOX::Direction::Generic
cauchyPtr
 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.
Teuchos::RCP
< NOX::MeritFunction::Generic
meritFuncPtr
 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)} $

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 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:

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

Definition at line 278 of file NOX_Solver_InexactTrustRegionBased.H.


Member Enumeration Documentation

Type of Trust Region algorithm to use.

Enumerator:
Standard  Basic trust region method for nonlinear systems (Nocedal and Wright?).
Inexact  Inexact Trust region WITHOUT minimization of the local linear model over the line segments.

Definition at line 339 of file NOX_Solver_InexactTrustRegionBased.H.

Return types for inner iteration status test.

Enumerator:
Converged  Converged.
Unconverged  Unconverged.
Failed  Failed by hitting minimum radius bound.

Definition at line 350 of file NOX_Solver_InexactTrustRegionBased.H.

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

Enumerator:
Newton  Use the Newton direction.
Cauchy  Use the Cauchy direction.
Dogleg  Use the doglog direction.

Definition at line 459 of file NOX_Solver_InexactTrustRegionBased.H.


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 
)

Constructor.

See reset() for description.

Definition at line 62 of file NOX_Solver_InexactTrustRegionBased.C.

References NOX::DeepCopy, init(), and NOX::ShapeCopy.

NOX::Solver::InexactTrustRegionBased::~InexactTrustRegionBased (  )  [virtual]

Destructor.

Definition at line 99 of file NOX_Solver_InexactTrustRegionBased.C.


Member Function Documentation

void NOX::Solver::InexactTrustRegionBased::reset ( const NOX::Abstract::Vector initial_guess,
const Teuchos::RCP< NOX::StatusTest::Generic > &  test 
) [virtual]

Resets the solver, sets a new status test, and sets a new initial guess.

Implements NOX::Solver::Generic.

Definition at line 243 of file NOX_Solver_InexactTrustRegionBased.C.

References checkType, dx, NOX::Utils::fill(), meritFuncPtr, newF, nIter, NOX::Utils::Parameters, paramsPtr, resetCounters(), solnPtr, status, testPtr, NOX::StatusTest::Unconverged, useCounters, and utils.

void NOX::Solver::InexactTrustRegionBased::reset ( const NOX::Abstract::Vector initial_guess  )  [virtual]

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::getStatus (  )  [virtual]

Check current convergence and failure status.

Implements NOX::Solver::Generic.

Definition at line 316 of file NOX_Solver_InexactTrustRegionBased.C.

References status.

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::step (  )  [virtual]

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::solve (  )  [virtual]

const Abstract::Group & NOX::Solver::InexactTrustRegionBased::getSolutionGroup (  )  const [virtual]

Return a reference to the current solution group.

Implements NOX::Solver::Generic.

Definition at line 1047 of file NOX_Solver_InexactTrustRegionBased.C.

References solnPtr.

const Abstract::Group & NOX::Solver::InexactTrustRegionBased::getPreviousSolutionGroup (  )  const [virtual]

Return a reference to the previous solution group.

Implements NOX::Solver::Generic.

Definition at line 1056 of file NOX_Solver_InexactTrustRegionBased.C.

References oldSolnPtr.

int NOX::Solver::InexactTrustRegionBased::getNumIterations (  )  const [virtual]

Get number of iterations.

Implements NOX::Solver::Generic.

Definition at line 1064 of file NOX_Solver_InexactTrustRegionBased.C.

References nIter.

const Teuchos::ParameterList & NOX::Solver::InexactTrustRegionBased::getList (  )  const [virtual]

Return a refernece to the solver parameters.

Implements NOX::Solver::Generic.

Definition at line 1073 of file NOX_Solver_InexactTrustRegionBased.C.

References paramsPtr.

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::iterateStandard (  )  [protected, virtual]

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::iterateInexact (  )  [protected, virtual]

void NOX::Solver::InexactTrustRegionBased::init (  )  [protected, virtual]

void NOX::Solver::InexactTrustRegionBased::printUpdate (  )  [protected, virtual]

void NOX::Solver::InexactTrustRegionBased::invalid ( const string &  param,
double  value 
) const [protected, virtual]

Print an error message and throw an error during parameter reads.

Definition at line 219 of file NOX_Solver_InexactTrustRegionBased.C.

References utils.

Referenced by init().

void NOX::Solver::InexactTrustRegionBased::throwError ( const string &  method,
const string &  mesage 
) const [protected, virtual]

Print an error message and throw an error.

Definition at line 231 of file NOX_Solver_InexactTrustRegionBased.C.

References utils.

Referenced by iterateInexact().

void NOX::Solver::InexactTrustRegionBased::resetCounters (  )  [protected, virtual]

NOX::StatusTest::StatusType NOX::Solver::InexactTrustRegionBased::checkStep ( const NOX::Abstract::Vector step,
double &  radius 
) [protected]

Check to see if the current step is acceptable. If not, it reduces the trust region radius accordingly.

Definition at line 1000 of file NOX_Solver_InexactTrustRegionBased.C.

References NOX::StatusTest::Converged.

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.

Definition at line 1135 of file NOX_Solver_InexactTrustRegionBased.C.

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

Referenced by iterateInexact(), and iterateStandard().


Member Data Documentation

Type of trust region algorithm to use.

Definition at line 347 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), and step().

Pointer to the global data object.

Definition at line 360 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init().

Current status of the trust region inner iteration.

Definition at line 366 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact().

Previous solution pointer.

Definition at line 372 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by getPreviousSolutionGroup(), iterateInexact(), and iterateStandard().

Current newton direction pointer.

Definition at line 375 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

Current cauchy direction pointer.

Definition at line 378 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

Extra vector used in computations.

Definition at line 381 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact().

Extra vector used in computations.

Definition at line 384 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact().

Extra vector used in computations.

Definition at line 387 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

Extra vector used in computations.

Definition at line 390 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

Stopping test.

Definition at line 393 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), printUpdate(), reset(), and step().

Teuchos::RCP<Teuchos::ParameterList> NOX::Solver::InexactTrustRegionBased::paramsPtr [protected]

Input parameters.

Definition at line 396 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by getList(), init(), iterateInexact(), reset(), and solve().

Inexact Newton utitilities.

Definition at line 399 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), and iterateInexact().

Newton Search Direction.

Definition at line 402 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), and iterateStandard().

Cauchy Search Direction.

Definition at line 405 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Radius of the trust region.

Definition at line 408 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), and printUpdate().

Minimum improvement ratio to accept step.

Definition at line 411 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Minimum trust region radius.

Definition at line 414 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Maximum trust region radius.

Definition at line 417 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

ratio < alpha triggers contraction

Definition at line 420 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

ratio > beta triggers expansion

Definition at line 423 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Expansion factor.

Definition at line 426 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Constraction factor.

Definition at line 429 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

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

Definition at line 433 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

Value of $ f $ at current solution.

Definition at line 436 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), printUpdate(), reset(), and step().

Value of $ f $ at previous solution.

Definition at line 438 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

norm(xnew - xold)

Definition at line 441 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateStandard(), printUpdate(), and reset().

Number of nonlinear iterations.

Definition at line 444 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by getNumIterations(), init(), iterateInexact(), iterateStandard(), printUpdate(), reset(), solve(), and step().

Current linear solve tolerance (inexact only).

Definition at line 447 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact().

Linear solve tolerance used in last iteration (inexact only).

Definition at line 450 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact().

Status of nonlinear solver.

Definition at line 453 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by getStatus(), init(), iterateInexact(), iterateStandard(), printUpdate(), reset(), solve(), and step().

Type of check to use for status tests. See NOX::StatusTest for more details.

Definition at line 456 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), iterateStandard(), reset(), and step().

Type of step to be taken.

Definition at line 470 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), and iterateStandard().

Stores merit function supplied by global data.

Definition at line 473 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), reset(), and step().

If set to true, the initial guess for the Newton direction computation will use the Cauchy direction as the initial guess.

Definition at line 476 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), and iterateInexact().

If set to true, statistics/counters will be output to the output list.

Definition at line 479 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by solve().

If set to true, counters will be stored by the solver.

Definition at line 482 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), iterateStandard(), reset(), and solve().

Counter for the number of cauchy steps taken.

Definition at line 485 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

Counter for the number of Newton steps taken.

Definition at line 488 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

Counter for the number of Dogleg steps taken.

Definition at line 491 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

Number of inner iterations required to adjust the trust region radius.

Definition at line 494 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

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.

Definition at line 497 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

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\|} $.

Definition at line 500 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by iterateInexact(), iterateStandard(), resetCounters(), and solve().

If set to true, the minimum improvement ratio condition uses an Ared/Pred approach.

Definition at line 503 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), iterateInexact(), and iterateStandard().

If set to true, the $ \tau $ parameter is minimized over the dogleg line segments instead of being computed at the trust regioin radius.

Definition at line 506 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by init(), and iterateInexact().

Pointer to a user defined NOX::Abstract::PrePostOperator object.

Definition at line 509 of file NOX_Solver_InexactTrustRegionBased.H.

Referenced by solve(), and step().


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

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