sgpp::optimization::optimizer::NLCG Class Reference

Gradient-based nonlinear conjugate gradient method. More...

#include <NLCG.hpp>

Inheritance diagram for sgpp::optimization::optimizer::NLCG:

Public Member Functions
void	clone (std::unique_ptr< UnconstrainedOptimizer > &clone) const override
double	getBeta () const
double	getEpsilon () const
double	getGamma () const
double	getRestartThreshold () const
double	getTolerance () const
	NLCG (const base::ScalarFunction &f, const base::ScalarFunctionGradient &fGradient, size_t maxItCount=DEFAULT_N, double beta=DEFAULT_BETA, double gamma=DEFAULT_GAMMA, double tolerance=DEFAULT_TOLERANCE, double epsilon=DEFAULT_EPSILON, double restartThreshold=DEFAULT_RESTART_THRESHOLD)
	Constructor.
	NLCG (const NLCG &other)
	Copy constructor.
void	optimize () override
	Pure virtual method for optimization of the objective function.
void	setBeta (double beta)
void	setEpsilon (double epsilon)
void	setGamma (double gamma)
void	setRestartThreshold (double restartThreshold)
void	setTolerance (double tolerance)
	~NLCG () override
	Destructor.
Public Member Functions inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
const base::DataMatrix &	getHistoryOfOptimalPoints () const
const base::DataVector &	getHistoryOfOptimalValues () const
size_t	getN () const
base::ScalarFunction &	getObjectiveFunction () const
base::ScalarFunctionGradient *	getObjectiveGradient () const
base::ScalarFunctionHessian *	getObjectiveHessian () const
const base::DataVector &	getOptimalPoint () const
double	getOptimalValue () const
const base::DataVector &	getStartingPoint () const
void	setN (size_t N)
virtual void	setObjectiveFunction (const base::ScalarFunction &f)
virtual void	setObjectiveGradient (const base::ScalarFunctionGradient *fGradient)
virtual void	setObjectiveHessian (const base::ScalarFunctionHessian *fHessian)
void	setStartingPoint (const base::DataVector &startingPoint)
	UnconstrainedOptimizer (const base::ScalarFunction &f, const base::ScalarFunctionGradient *fGradient, const base::ScalarFunctionHessian *fHessian, size_t N=DEFAULT_N)
	Constructor.
	UnconstrainedOptimizer (const UnconstrainedOptimizer &other)
	Copy constructor.
virtual	~UnconstrainedOptimizer ()
	Destructor.

Static Public Attributes
static constexpr double	DEFAULT_BETA = 0.5
	default beta (parameter for Armijo's rule)
static constexpr double	DEFAULT_EPSILON = 1e-18
	default epsilon (parameter for Armijo's rule)
static constexpr double	DEFAULT_GAMMA = 1e-2
	default gamma (parameter for Armijo's rule)
static constexpr double	DEFAULT_RESTART_THRESHOLD = 0.1
	default restart threshold
static constexpr double	DEFAULT_TOLERANCE = 1e-8
	default tolerance (parameter for Armijo's rule)
Static Public Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
static const size_t	DEFAULT_N = 1000
	default maximal number of iterations or function evaluations

Protected Attributes
double	alpha
	restart threshold
double	beta
	beta (parameter for Armijo's rule)
double	eps
	epsilon (parameter for Armijo's rule)
double	gamma
	gamma (parameter for Armijo's rule)
double	tol
	tolerance (parameter for Armijo's rule)
Protected Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
std::unique_ptr< base::ScalarFunction >	f
	objective function
std::unique_ptr< base::ScalarFunctionGradient >	fGradient
	objective function gradient
std::unique_ptr< base::ScalarFunctionHessian >	fHessian
	objective function Hessian
base::DataVector	fHist
	search history vector (optimal values)
double	fOpt
	result of optimization (optimal function value)
size_t	N
	maximal number of iterations or function evaluations
base::DataVector	x0
	starting point
base::DataMatrix	xHist
	search history matrix (optimal points)
base::DataVector	xOpt
	result of optimization (location of optimum)

Detailed Description

Gradient-based nonlinear conjugate gradient method.

The method is restarted with the steepest descent direction if the normalized absolute value of the inner product of two successive gradients exceeds a "restart threshold" \(\alpha\).

Constructor & Destructor Documentation

NLCG() [1/2]

sgpp::optimization::optimizer::NLCG::NLCG	(	const base::ScalarFunction &	f,
		const base::ScalarFunctionGradient &	fGradient,
		size_t	maxItCount = DEFAULT_N,
		double	beta = DEFAULT_BETA,
		double	gamma = DEFAULT_GAMMA,
		double	tolerance = DEFAULT_TOLERANCE,
		double	epsilon = DEFAULT_EPSILON,
		double	restartThreshold = DEFAULT_RESTART_THRESHOLD
	)

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)
restartThreshold	restart threshold

NLCG() [2/2]

sgpp::optimization::optimizer::NLCG::NLCG

(

const NLCG &

other

)

Copy constructor.

Parameters

other

optimizer to be copied

~NLCG()

sgpp::optimization::optimizer::NLCG::~NLCG ( )

override

Destructor.

Member Function Documentation

clone()

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

overridevirtual

Parameters

[out]

clone

pointer to cloned object

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

References clone().

Referenced by clone().

getBeta()

double sgpp::optimization::optimizer::NLCG::getBeta

(

)

const

Returns

beta (parameter for Armijo's rule)

References beta.

getEpsilon()

double sgpp::optimization::optimizer::NLCG::getEpsilon

(

)

const

Returns

epsilon (parameter for Armijo's rule)

References eps.

getGamma()

double sgpp::optimization::optimizer::NLCG::getGamma

(

)

const

Returns

gamma (parameter for Armijo's rule)

References gamma.

getRestartThreshold()

double sgpp::optimization::optimizer::NLCG::getRestartThreshold

(

)

const

Returns

restart threshold

References alpha.

getTolerance()

double sgpp::optimization::optimizer::NLCG::getTolerance

(

)

const

Returns

tolerance (parameter for Armijo's rule)

References tol.

optimize()

void sgpp::optimization::optimizer::NLCG::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 alpha, sgpp::base::DataVector::append(), sgpp::base::DataMatrix::appendRow(), beta, sgpp::base::DataVector::dotProduct(), eps, sgpp::optimization::optimizer::UnconstrainedOptimizer::f, sgpp::optimization::optimizer::UnconstrainedOptimizer::fGradient, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, gamma, sgpp::base::Printer::getInstance(), sgpp::base::DataVector::l2Norm(), sgpp::optimization::optimizer::lineSearchArmijo(), sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::base::Printer::printStatusBegin(), sgpp::base::Printer::printStatusEnd(), sgpp::base::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), 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::NLCG::setBeta

(

double

beta

)

Parameters

beta	beta (parameter for Armijo's rule)

References beta.

setEpsilon()

void sgpp::optimization::optimizer::NLCG::setEpsilon

(

double

epsilon

)

Parameters

epsilon

epsilon (parameter for Armijo's rule)

References eps.

setGamma()

void sgpp::optimization::optimizer::NLCG::setGamma

(

double

gamma

)

Parameters

gamma

gamma (parameter for Armijo's rule)

References gamma.

setRestartThreshold()

void sgpp::optimization::optimizer::NLCG::setRestartThreshold

(

double

restartThreshold

)

Parameters

restartThreshold

restart threshold

References alpha.

setTolerance()

void sgpp::optimization::optimizer::NLCG::setTolerance

(

double

tolerance

)

Parameters

tolerance

tolerance (parameter for Armijo's rule)

References tol.

Member Data Documentation

alpha

double sgpp::optimization::optimizer::NLCG::alpha

protected

restart threshold

Referenced by python.learner.Learner.Learner::doLearningIteration(), getRestartThreshold(), python.learner.Learner.Learner::learnData(), python.learner.Learner.Learner::learnDataWithTest(), python.uq.learner.Interpolant.Interpolant::learnDataWithTest(), optimize(), python.uq.dists.SGDEdist.SGDEdist::pdf(), setRestartThreshold(), and python.uq.dists.SGDEdist.SGDEdist::toJson().

beta

double sgpp::optimization::optimizer::NLCG::beta

protected

beta (parameter for Armijo's rule)

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

DEFAULT_BETA

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

staticconstexpr

default beta (parameter for Armijo's rule)

DEFAULT_EPSILON

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

staticconstexpr

default epsilon (parameter for Armijo's rule)

DEFAULT_GAMMA

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

staticconstexpr

default gamma (parameter for Armijo's rule)

DEFAULT_RESTART_THRESHOLD

constexpr double sgpp::optimization::optimizer::NLCG::DEFAULT_RESTART_THRESHOLD = 0.1

staticconstexpr

default restart threshold

DEFAULT_TOLERANCE

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

staticconstexpr

default tolerance (parameter for Armijo's rule)

eps

double sgpp::optimization::optimizer::NLCG::eps

protected

epsilon (parameter for Armijo's rule)

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

gamma

double sgpp::optimization::optimizer::NLCG::gamma

protected

gamma (parameter for Armijo's rule)

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

tol

double sgpp::optimization::optimizer::NLCG::tol

protected

tolerance (parameter for Armijo's rule)

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

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

• optimization/src/sgpp/optimization/optimizer/unconstrained/NLCG.hpp
• optimization/src/sgpp/optimization/optimizer/unconstrained/NLCG.cpp