HCL_UMinTR

class HCL_UMinTR_d : public HCL_UMin_d

The class HCL_UMinTR_d implements a generic algorithm for solving unconstrained minimization problems using a trust region method

Inheritance:

Public Methods

Inherited from HCL_UMin_d:

Public
enum Return values for the method Minimize.

PossibleMinimizer
Possible local minimizer
PossibleConvergence
Possible convergence
LineSearchFailed
Line search failed
PossibleDivergence
Possible divergence
IterationLimit
Iteration limit reached
InaccurateGradient
Possible inaccurate gradient calculation

Inherited from HCL_Base:

Public Methods
void IncCount() const
void DecCount() const
int Count() const

Documentation

The class HCL_UMinTR_d implements a generic algorithm for solving unconstrained minimization problems using a trust region method. A HCL_TrustRegionSolver_d, which implements an algorithm for solving the trust region subproblem, is required to construct the minimizer. If the user does not provide a trust region solver, the HCL_TRCG_d, which implements the Steihaug-Toint algorithm, is used by default. Note that the Steihaug-Toint algorithm is intended for large-scale problems.
The three important methods of this class are:

Minimize This method takes a HCL_Functional_d and a starting point, and attempts to locate a local minimizer of the functional. The return value of the method is the termination code, which indicates why the algorithm terminated. See the documentation for the termination codes for details.
Parameters This method returns a reference to the parameter table, and allows the programmer to access or change the parameters that control the iteration. See the documentation on input parameters for details about algorithmic parameters.
LastEval This method returns a reference to the evaluation object at the best point found by the algorithm, thus giving the calling routine access to the function value, gradient, and Hessian at the final point. It is an error to call LastEval before Minimize.

int MaxItn

(100) maximum number of iterations

double Typf

(1.0) Typical value of the functional near the solution. Setting this makes the gradient stopping tolerance more meaningful.

double TypxNorm

(1.0) Typical norm of the unknown vector x near the solution. Setting this makes the gradient stopping tolerance more meaningful.

double GradTol

(1.0e-2) Gradient tolerance. The algorithm attempts to locate a point where the relative gradient norm (i.e. the norm of the gradient scaled by the size of the vector x and by f(x)) is less than this value.

double MinStep

(1e-20) Minimum allowable step. If the algorithm takes a (relative) step less than this value in norm, it halts and reports "Possible convergence".

double MaxStep

(1e+20) Maximum allowable step. If the algorithm takes too many consecutive steps of length MaxStep, it assumes that the iterates are diverging and reports "Possible divergence".

int CscMaxLimit

(5) Maximum number of steps of length MaxStep allowed before the algorithm decides that the iterates are diverging

int DispFlag

(0) Display level. This determines how much information should be displayed during the execution of the algorithm. Possible values are: 0 - No output; 1 - Function value and gradient norm after final iteration; 2 - Function value and gradient norm after every iteration.

int DumpFlag

(0) Dump level. This determines how much information should be sent to the dump file during the execution of the algorithm. Possible values are: 0 - No output; 1 - Function value and gradient norm after final iteration; 2 - Function value and gradient norm after every iteration.

char DumpFile[81]

(HCL_UMin_lbfgs.DumpFile) Dump file name.

int DispPrecision

(6) Display precision---the number of digits sent to the screen

int DumpPrecision

(6) Dump precision---the number of digits sent to the dump file

int TraceSteps

(0) If nonzero, the iterates are sent to a file using the Write method from the vector class

char StepFile[81]

(HCL_UMinTR.StepFile) File name for recording iterates.

double LowerTol

(1e-1) Tolerance for reducing the trust region radius. If the ratio of the actual to the predicted reduction falls below LowerTol, the radius is cut in half.

double UpperTol

(9e-1) Tolerance for increasing the trust region radius. If the ratio of the actual to the predicted reduction is greater than UpperTol, the radius is doubled.

double Delta

(1.0) Initial trust region radius.

HCL_UMinTR_d( HCL_TrustRegionSolver_d * trs=NULL, char * fname=NULL )

Usual constructor

Parameters:: trs - TrustRegionSolver class (optional). If no trust region solver is specified, then the Steihaug-Toint algorithm (HCL_TRCG_d) will be used.
fname - Parameter file name or NULL. If given, this file contains algorithmic parameters (such as stopping tolerances), a full list of which is given elsewhere in the documentation of this class. For example, to set the maximum number of iterations to 100, the file should contain a line of the form UMinTR::MaxItn = 100 or, alternately, UMin::MaxItn = 100. If the trust region solver is not provided, then this file will also be passed to the HCL_TRCG_d constructor, and so can contain entries such as TRSolver::DispFlag = 1.

Table& Parameters() const

Access to parameter table. Algorithmic parameters can be accessed with Parameters().GetValue( "NAME",val ) or changed with Parameters().PutValue( "NAME",val ).

virtual HCL_EvaluateFunctional_d& LastEval() const

LastEval returns a reference to the functional's evaluation object at the most recent point. Thus, after the minimization has completed, the calling routine has access to the last function value, gradient, and Hessian.

virtual void SetScaling( HCL_LinearOp_d * S, HCL_LinearSolver_d * lsolver=NULL )

SetScaling defines a new inner product in terms of a symmetric, positive definite operator S: <x,y> = (x,Sy)

virtual void UnSetScaling()

UnSetScaling returns the inner product to the default.

int Minimize( HCL_Functional_d & f, HCL_Vector_d & x )

Minimize attempts to find a local minimizer of the functional f, using x as a starting guess

virtual ostream& Write( ostream & str ) const

Prints description of the object

This class has no child classes.

alphabetic index hierarchy of classes

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(c)opyright by Malte Zöckler, Roland Wunderling
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	HCL_UMinTR_d ( HCL_TrustRegionSolver_d * trs=NULL, char * fname=NULL ) Usual constructor
Table&	Parameters () const Access to parameter table
virtual HCL_EvaluateFunctional_d&	LastEval () const LastEval returns a reference to the functional's evaluation object at the most recent point
virtual void	SetScaling ( HCL_LinearOp_d * S, HCL_LinearSolver_d * lsolver=NULL ) SetScaling defines a new inner product in terms of a symmetric, positive definite operator S: <x,y> = (x,Sy)
virtual void	UnSetScaling () UnSetScaling returns the inner product to the default.
int	Minimize ( HCL_Functional_d & f, HCL_Vector_d & x ) Minimize attempts to find a local minimizer of the functional f, using x as a starting guess
virtual ostream&	Write ( ostream & str ) const Prints description of the object