Gradient-based method of steepest descent. More...

#include <GradientDescent.hpp>

Inheritance diagram for sgpp::optimization::optimizer::GradientDescent:

Public Member Functions
void	clone (std::unique_ptr< UnconstrainedOptimizer > &clone) const override

double	getBeta () const

double	getEpsilon () const

double	getGamma () const

ScalarFunctionGradient &	getObjectiveGradient () const

double	getTolerance () const

	GradientDescent (const ScalarFunction &f, const ScalarFunctionGradient &fGradient, size_t maxItCount=DEFAULT_MAX_IT_COUNT, double beta=DEFAULT_BETA, double gamma=DEFAULT_GAMMA, double tolerance=DEFAULT_TOLERANCE, double epsilon=DEFAULT_EPSILON)
	Constructor. More...

	GradientDescent (const GradientDescent &other)
	Copy constructor. More...

void	optimize () override
	Pure virtual method for optimization of the objective function. More...

void	setBeta (double beta)

void	setEpsilon (double epsilon)

void	setGamma (double gamma)

void	setTolerance (double tolerance)

	~GradientDescent () override
	Destructor. More...

Public Member Functions inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
const base::DataMatrix &	getHistoryOfOptimalPoints () const

const base::DataVector &	getHistoryOfOptimalValues () const

size_t	getN () const

ScalarFunction &	getObjectiveFunction () const

const base::DataVector &	getOptimalPoint () const

double	getOptimalValue () const

const base::DataVector &	getStartingPoint () const

void	setN (size_t N)

void	setStartingPoint (const base::DataVector &startingPoint)

	UnconstrainedOptimizer (const ScalarFunction &f, size_t N=DEFAULT_N)
	Constructor. More...

	UnconstrainedOptimizer (const UnconstrainedOptimizer &other)
	Copy constructor. More...

virtual	~UnconstrainedOptimizer ()
	Destructor. More...

Static Public Attributes
static constexpr double	DEFAULT_BETA = 0.5
	default beta (parameter for Armijo's rule) More...

static constexpr double	DEFAULT_EPSILON = 1e-18
	default epsilon (parameter for Armijo's rule) More...

static constexpr double	DEFAULT_GAMMA = 1e-2
	default gamma (parameter for Armijo's rule) More...

static const size_t	DEFAULT_MAX_IT_COUNT = 2000
	default maximal number of iterations More...

static constexpr double	DEFAULT_TOLERANCE = 1e-8
	default tolerance (parameter for Armijo's rule) More...

Static Public Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
static const size_t	DEFAULT_N = 1000
	default maximal number of iterations or function evaluations More...

Protected Attributes
double	beta
	beta (parameter for Armijo's rule) More...

double	eps
	epsilon (parameter for Armijo's rule) More...

std::unique_ptr< ScalarFunctionGradient >	fGradient
	objective function gradient More...

double	gamma
	gamma (parameter for Armijo's rule) More...

double	tol
	tolerance (parameter for Armijo's rule) More...

Protected Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
std::unique_ptr< ScalarFunction >	f
	objective function More...

base::DataVector	fHist
	search history vector (optimal values) More...

double	fOpt
	result of optimization (optimal function value) More...

size_t	N
	maximal number of iterations or function evaluations More...

base::DataVector	x0
	starting point More...

base::DataMatrix	xHist
	search history matrix (optimal points) More...

base::DataVector	xOpt
	result of optimization (location of optimum) More...

Detailed Description

Gradient-based method of steepest descent.

Constructor & Destructor Documentation

◆ GradientDescent() [1/2]

sgpp::optimization::optimizer::GradientDescent::GradientDescent	(	const ScalarFunction &	f,
		const ScalarFunctionGradient &	fGradient,
		size_t	maxItCount = `DEFAULT_MAX_IT_COUNT`,
		double	beta = `DEFAULT_BETA`,
		double	gamma = `DEFAULT_GAMMA`,
		double	tolerance = `DEFAULT_TOLERANCE`,
		double	epsilon = `DEFAULT_EPSILON`
	)

Constructor.

Parameters

f	objective function
fGradient	objective function gradient
maxItCount	maximal number of iterations
beta	beta (parameter for Armijo's rule)
gamma	gamma (parameter for Armijo's rule)
tolerance	tolerance (parameter for Armijo's rule)
epsilon	epsilon (parameter for Armijo's rule)

References sgpp::optimization::ScalarFunctionGradient::clone().

Referenced by clone().

◆ GradientDescent() [2/2]

sgpp::optimization::optimizer::GradientDescent::GradientDescent ( const GradientDescent & other )

Copy constructor.

Parameters

other optimizer to be copied

References fGradient.

◆ ~GradientDescent()

sgpp::optimization::optimizer::GradientDescent::~GradientDescent ( )

override

Destructor.

Member Function Documentation

◆ clone()

void sgpp::optimization::optimizer::GradientDescent::clone ( std::unique_ptr< UnconstrainedOptimizer > & clone ) const

overridevirtual

Parameters

[out] clone pointer to cloned object

Implements sgpp::optimization::optimizer::UnconstrainedOptimizer.

References GradientDescent().

◆ getBeta()

double sgpp::optimization::optimizer::GradientDescent::getBeta ( ) const

Returns: beta (parameter for Armijo's rule)

References beta.

◆ getEpsilon()

double sgpp::optimization::optimizer::GradientDescent::getEpsilon ( ) const

Returns: epsilon (parameter for Armijo's rule)

References eps.

◆ getGamma()

double sgpp::optimization::optimizer::GradientDescent::getGamma ( ) const

Returns: gamma (parameter for Armijo's rule)

References gamma.

◆ getObjectiveGradient()

ScalarFunctionGradient & sgpp::optimization::optimizer::GradientDescent::getObjectiveGradient ( ) const

Returns: objective function gradient

References fGradient.

◆ getTolerance()

double sgpp::optimization::optimizer::GradientDescent::getTolerance ( ) const

Returns: tolerance (parameter for Armijo's rule)

References tol.

◆ optimize()

void sgpp::optimization::optimizer::GradientDescent::optimize ( )

overridevirtual

Pure virtual method for optimization of the objective function.

The result of the optimization process can be obtained by member functions, e.g., getOptimalPoint() and getOptimalValue().

Implements sgpp::optimization::optimizer::UnconstrainedOptimizer.

References sgpp::base::DataVector::append(), sgpp::base::DataMatrix::appendRow(), beta, eps, sgpp::optimization::optimizer::UnconstrainedOptimizer::f, fGradient, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, gamma, sgpp::optimization::Printer::getInstance(), sgpp::base::DataVector::l2Norm(), sgpp::optimization::optimizer::lineSearchArmijo(), sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::optimization::Printer::printStatusBegin(), sgpp::optimization::Printer::printStatusEnd(), sgpp::optimization::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), create_scripts::s, tol, sgpp::base::DataVector::toString(), sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

◆ setBeta()

void sgpp::optimization::optimizer::GradientDescent::setBeta ( double beta )

Parameters

beta	beta (parameter for Armijo's rule)

References beta.

◆ setEpsilon()

void sgpp::optimization::optimizer::GradientDescent::setEpsilon ( double epsilon )

Parameters

epsilon epsilon (parameter for Armijo's rule)

References eps.

◆ setGamma()

void sgpp::optimization::optimizer::GradientDescent::setGamma ( double gamma )

Parameters

gamma gamma (parameter for Armijo's rule)

References gamma.

◆ setTolerance()

void sgpp::optimization::optimizer::GradientDescent::setTolerance ( double tolerance )

Parameters

tolerance tolerance (parameter for Armijo's rule)

References tol.

Member Data Documentation

◆ beta

double sgpp::optimization::optimizer::GradientDescent::beta

protected

beta (parameter for Armijo's rule)

Referenced by getBeta(), optimize(), and setBeta().

◆ DEFAULT_BETA

constexpr double sgpp::optimization::optimizer::GradientDescent::DEFAULT_BETA = 0.5

static

default beta (parameter for Armijo's rule)

◆ DEFAULT_EPSILON

constexpr double sgpp::optimization::optimizer::GradientDescent::DEFAULT_EPSILON = 1e-18

static

default epsilon (parameter for Armijo's rule)

◆ DEFAULT_GAMMA

constexpr double sgpp::optimization::optimizer::GradientDescent::DEFAULT_GAMMA = 1e-2

static

default gamma (parameter for Armijo's rule)

◆ DEFAULT_MAX_IT_COUNT

const size_t sgpp::optimization::optimizer::GradientDescent::DEFAULT_MAX_IT_COUNT = 2000

static

default maximal number of iterations

◆ DEFAULT_TOLERANCE

constexpr double sgpp::optimization::optimizer::GradientDescent::DEFAULT_TOLERANCE = 1e-8

static

default tolerance (parameter for Armijo's rule)

◆ eps

double sgpp::optimization::optimizer::GradientDescent::eps

protected

epsilon (parameter for Armijo's rule)

Referenced by getEpsilon(), optimize(), and setEpsilon().

◆ fGradient

std::unique_ptr<ScalarFunctionGradient> sgpp::optimization::optimizer::GradientDescent::fGradient

protected

objective function gradient

Referenced by getObjectiveGradient(), GradientDescent(), and optimize().

◆ gamma

double sgpp::optimization::optimizer::GradientDescent::gamma

protected

gamma (parameter for Armijo's rule)

Referenced by getGamma(), optimize(), and setGamma().

◆ tol

double sgpp::optimization::optimizer::GradientDescent::tol

protected

tolerance (parameter for Armijo's rule)

Referenced by getTolerance(), optimize(), and setTolerance().

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

optimization/src/sgpp/optimization/optimizer/unconstrained/GradientDescent.hpp
optimization/src/sgpp/optimization/optimizer/unconstrained/GradientDescent.cpp

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ GradientDescent() [1/2]

◆ GradientDescent() [2/2]

◆ ~GradientDescent()

Member Function Documentation

◆ clone()

◆ getBeta()

◆ getEpsilon()

◆ getGamma()

◆ getObjectiveGradient()

◆ getTolerance()

◆ optimize()

◆ setBeta()

◆ setEpsilon()

◆ setGamma()

◆ setTolerance()

Member Data Documentation

◆ beta

◆ DEFAULT_BETA

◆ DEFAULT_EPSILON

◆ DEFAULT_GAMMA

◆ DEFAULT_MAX_IT_COUNT

◆ DEFAULT_TOLERANCE

◆ eps

◆ fGradient

◆ gamma

◆ tol