Newton descent method. More...

#include <NewtonDescent.hpp>

Collaboration diagram for ipo::detail::NewtonDescent:

Classes
class	Parameters
	Line search parameters. More...

class	Stopping
	This class allows us to test suitable stopping conditions. More...

Public Types
enum	StoppingCondition { StoppingCondition::gradTol, StoppingCondition::stepTol, StoppingCondition::iterMax, StoppingCondition::noStopping }
	Enumeration for stopping conditions. More...

Public Member Functions
	NewtonDescent (ipo_function::Function &function, ipo_function::DerivativesEstimates &de, gsl::matrix const equalityConstraintsMatrix=gsl::matrix(), gsl::vector const equalityConstraintsBounds=gsl::vector())
	The constructor needs a Function and a DerivativesEstimates (which may be identical). More...

double	operator() (gsl::vector &x, double objectiveValue)
	The function object operator. More...

void	setFunctionScale (double const functionScale)
	Set the scaling factor for output of function values. More...

StoppingCondition	getLastStoppingCondition () const
	Get Last stopping condition. More...

Parameters &	getParameters ()
	Get parameters by reference. More...

LineSearch::Parameters &	getLineSearchParameters ()
	Get line search parameters by reference. More...

Protected Attributes
StoppingCondition	lastStoppingCondition = StoppingCondition::noStopping
	Last stopping condition. More...

gsl::matrix const	equalityConstraintsMatrix
	This must be set in the constructor. More...

ipo_function::Function &	function
	We need a copy of the function so that we can use LineSearch. More...

ipo_function::DerivativesEstimates &	de
	The object containing the function and derivatives estimates. More...

LineSearch	lineSearch
	We need a LineSearch object: backtracking line search. More...

double	functionScale
	Scaling factor for output of function values. More...

gsl::matrix	A
	This matrix is used in singular value decompostion and its size is set in constructor if it is needed. More...

gsl::matrix	V
	This matrix is used in singular value decompostion and its size is set in constructor if it is needed. More...

gsl::vector	S
	This vector is used in singular value decompostion and its size is set in constructor if it is needed. More...

gsl::vector	work
	This vector is used in singular value decompostion and its size is set in constructor if it is needed. More...

gsl::vector	b
	This vector is used in singular value decompostion and its size is set in constructor if it is needed. More...

Private Attributes
Parameters	parameters

Friends
class	Stopping

Detailed Description

Newton descent method.

An object of this class takes a function as its parameter and attempts to use Newton descent to minimise the function. The stopping criterion is: stop when the absolute size of the estimated gradient is no more than the square root of eta. The default value for eta is square root of machine epsilon.

The class uses DerivativesEstimates to estimate gradients and Hessians numerically and is designed to work well when the function has a single local minimum and continuous first and second derivates.

The function can summarise its own progress through the outputStream parameter. Its default value of nullptr prevents output.

Definition at line 50 of file NewtonDescent.hpp.

Member Enumeration Documentation

enum ipo::detail::NewtonDescent::StoppingCondition

strong

Enumeration for stopping conditions.

Enumerator
gradTol	Gradient tolerance reached.
stepTol	Relative step size tolerance reached.
iterMax	Maximum iterations reached.
noStopping	No stopping condition reached.

Definition at line 256 of file NewtonDescent.hpp.

Constructor & Destructor Documentation

NewtonDescent::NewtonDescent	(	ipo_function::Function &	function,
		ipo_function::DerivativesEstimates &	de,
		gsl::matrix const	equalityConstraintsMatrix = `gsl::matrix()`,
		gsl::vector const	equalityConstraintsBounds = `gsl::vector()`
	)

The constructor needs a Function and a DerivativesEstimates (which may be identical).

It also needs a matrix and bounds for equality constraints if there are any. If a matrix and vector are supplied they must have numbers of columns or entries equal and equal to the length of vector expected by function and de

Parameters

function	A copy of the function so that we can use LineSearch
de	An object that allows us to estimate function value and first and second derivatives
equalityConstraintsMatrix	A matrix for the equality constraints
equalityConstraintsBounds	A vector for the equality constraint bounds

Exceptions

IPOException if equalityConstraintsMatrix and equalityConstraintsBounds are inconsistent

Definition at line 51 of file NewtonDescent.cc.

Member Function Documentation

NewtonDescent::StoppingCondition NewtonDescent::getLastStoppingCondition ( ) const

Get Last stopping condition.

Returns: Stopping condition of last call to operator()()

Definition at line 295 of file NewtonDescent.cc.

References lastStoppingCondition.

LineSearch::Parameters & NewtonDescent::getLineSearchParameters ( )

Get line search parameters by reference.

Returns: parameters

Definition at line 38 of file NewtonDescent.cc.

References ipo::detail::LineSearch::getParameters(), and lineSearch.

NewtonDescent::Parameters & NewtonDescent::getParameters ( )

Get parameters by reference.

Returns: parameters

Definition at line 35 of file NewtonDescent.cc.

References parameters.

Referenced by ipo::detail::NewtonDescent::Stopping::operator()(), and ipo::Model::optimise().

double NewtonDescent::operator()	(	gsl::vector &	x,
		double	objectiveValue
	)

The function object operator.

This operates on a vector x. On return x is replaced with its new value.

Parameters

x	The vector
objectiveValue	The objective function evaluated at x

Returns: The objective function evaluated at final value of x

Definition at line 95 of file NewtonDescent.cc.

References A, b, de, equalityConstraintsMatrix, functionScale, ipo::detail::NewtonDescent::Parameters::getOutputStream(), ipo::detail::NewtonDescent::Parameters::getPhaseI(), ipo::detail::NewtonDescent::Parameters::getVectorDigits(), ipo_function::GradientEstimate::gradient(), ipo_function::DerivativesEstimates::hessian(), IPOE, lineSearch, ipo::detail::modelHessian(), parameters, S, ipo::detail::LineSearch::setFunctionScale(), ipo_function::GradientEstimate::setVector(), V, ipo_function::GradientEstimate::value(), and work.

void ipo::detail::NewtonDescent::setFunctionScale ( double const functionScale )

inline

Set the scaling factor for output of function values.

This is used in InteriorPoint to show the value of the original function.

Parameters

functionScale The new value

Definition at line 251 of file NewtonDescent.hpp.

References functionScale.

Friends And Related Function Documentation

friend class Stopping

friend

Definition at line 279 of file NewtonDescent.hpp.

Member Data Documentation

gsl::matrix ipo::detail::NewtonDescent::A

protected

This matrix is used in singular value decompostion and its size is set in constructor if it is needed.

Definition at line 311 of file NewtonDescent.hpp.

Referenced by operator()().

gsl::vector ipo::detail::NewtonDescent::b

protected

This vector is used in singular value decompostion and its size is set in constructor if it is needed.

Definition at line 331 of file NewtonDescent.hpp.

Referenced by operator()().

ipo_function::DerivativesEstimates& ipo::detail::NewtonDescent::de

protected

The object containing the function and derivatives estimates.

Definition at line 298 of file NewtonDescent.hpp.

Referenced by operator()().

gsl::matrix const ipo::detail::NewtonDescent::equalityConstraintsMatrix

protected

This must be set in the constructor.

Set to null matrix or to have 0 rows to solve a problem without equality constraints. Otherwise set these equality constraints.

Definition at line 290 of file NewtonDescent.hpp.

Referenced by operator()().

ipo_function::Function& ipo::detail::NewtonDescent::function

protected

We need a copy of the function so that we can use LineSearch.

Definition at line 294 of file NewtonDescent.hpp.

double ipo::detail::NewtonDescent::functionScale

protected

Scaling factor for output of function values.

Definition at line 306 of file NewtonDescent.hpp.

Referenced by operator()(), and setFunctionScale().

StoppingCondition ipo::detail::NewtonDescent::lastStoppingCondition = StoppingCondition::noStopping

mutableprotected

Last stopping condition.

Definition at line 284 of file NewtonDescent.hpp.

Referenced by getLastStoppingCondition().

LineSearch ipo::detail::NewtonDescent::lineSearch

protected

We need a LineSearch object: backtracking line search.

Definition at line 302 of file NewtonDescent.hpp.

Referenced by getLineSearchParameters(), and operator()().

Parameters ipo::detail::NewtonDescent::parameters

private

Definition at line 220 of file NewtonDescent.hpp.

Referenced by getParameters(), and operator()().

gsl::vector ipo::detail::NewtonDescent::S

protected

This vector is used in singular value decompostion and its size is set in constructor if it is needed.

Definition at line 321 of file NewtonDescent.hpp.

Referenced by operator()().

gsl::matrix ipo::detail::NewtonDescent::V

protected

This matrix is used in singular value decompostion and its size is set in constructor if it is needed.

Definition at line 316 of file NewtonDescent.hpp.

Referenced by operator()().

gsl::vector ipo::detail::NewtonDescent::work

protected

This vector is used in singular value decompostion and its size is set in constructor if it is needed.

Definition at line 326 of file NewtonDescent.hpp.

Referenced by operator()().

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

Classes

Public Types

Public Member Functions

Protected Attributes

Private Attributes

Friends

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation