sgpp::optimization::optimizer::Newton Class Reference

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

#include <Newton.hpp>

Inheritance diagram for sgpp::optimization::optimizer::Newton:

Public Member Functions
void	clone (std::unique_ptr< UnconstrainedOptimizer > &clone) const override
double	getAlpha1 () const
double	getAlpha2 () const
double	getBeta () const
double	getEpsilon () const
double	getGamma () const
ScalarFunctionHessian &	getObjectiveHessian () const
double	getP () const
double	getTolerance () const
	Newton (const ScalarFunction &f, const ScalarFunctionHessian &fHessian, size_t maxItCount=DEFAULT_N, double beta=DEFAULT_BETA, double gamma=DEFAULT_GAMMA, double tolerance=DEFAULT_TOLERANCE, double epsilon=DEFAULT_EPSILON, double alpha1=DEFAULT_ALPHA1, double alpha2=DEFAULT_ALPHA2, double p=DEFAULT_P)
	Constructor. More...
	Newton (const ScalarFunction &f, const ScalarFunctionHessian &fHessian, size_t maxItCount, double beta, double gamma, double tolerance, double epsilon, double alpha1, double alpha2, double p, const sle_solver::SLESolver &sleSolver)
	Constructor. More...
	Newton (const Newton &other)
	Copy constructor. More...
void	optimize () override
	Pure virtual method for optimization of the objective function. More...
void	setAlpha1 (double alpha1)
void	setAlpha2 (double alpha2)
void	setBeta (double beta)
void	setEpsilon (double epsilon)
void	setGamma (double gamma)
void	setP (double p)
void	setTolerance (double tolerance)
	~Newton () 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_ALPHA1 = 1e-6
	default steepest descent restart parameter 1 More...
static constexpr double	DEFAULT_ALPHA2 = 1e-6
	default steepest descent restart parameter 2 More...
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 constexpr double	DEFAULT_P = 0.1
	default steepest descent restart exponent 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	alpha1
	steepest descent restart parameter 1 More...
double	alpha2
	steepest descent restart parameter 2 More...
double	beta
	beta (parameter for Armijo's rule) More...
const sle_solver::GaussianElimination	defaultSleSolver
	default linear solver More...
double	eps
	epsilon (parameter for Armijo's rule) More...
std::unique_ptr< ScalarFunctionHessian >	fHessian
	objective function Hessian More...
double	gamma
	gamma (parameter for Armijo's rule) More...
double	p
	steepest descent restart exponent More...
const sle_solver::SLESolver &	sleSolver
	linear solver 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 nonlinear conjugate gradient method.

The method is restarted with the steepest descent direction if the inner product of negated gradient and search direction is not big enough (criterion depending on three parameters).

Constructor & Destructor Documentation

Newton() [1/3]

sgpp::optimization::optimizer::Newton::Newton	(	const ScalarFunction &	f,
		const ScalarFunctionHessian &	fHessian,
		size_t	maxItCount = DEFAULT_N,
		double	beta = DEFAULT_BETA,
		double	gamma = DEFAULT_GAMMA,
		double	tolerance = DEFAULT_TOLERANCE,
		double	epsilon = DEFAULT_EPSILON,
		double	alpha1 = DEFAULT_ALPHA1,
		double	alpha2 = DEFAULT_ALPHA2,
		double	p = DEFAULT_P
	)

Constructor.

By default, GaussianElimination is used to solve the linear systems.

Parameters

f	objective function
fHessian	objective function Hessian
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)
alpha1	steepest descent restart parameter 1
alpha2	steepest descent restart parameter 2
p	steepest descent restart exponent

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

Referenced by clone().

Newton() [2/3]

sgpp::optimization::optimizer::Newton::Newton	(	const ScalarFunction &	f,
		const ScalarFunctionHessian &	fHessian,
		size_t	maxItCount,
		double	beta,
		double	gamma,
		double	tolerance,
		double	epsilon,
		double	alpha1,
		double	alpha2,
		double	p,
		const sle_solver::SLESolver &	sleSolver
	)

Constructor.

Do not destruct the solver before this object!

Parameters

f	objective function
fHessian	objective function Hessian
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)
alpha1	steepest descent restart parameter 1
alpha2	steepest descent restart parameter 2
p	steepest descent restart exponent
sleSolver	reference to linear solver for solving the linear systems (Hessian as coefficient matrix)

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

Newton() [3/3]

sgpp::optimization::optimizer::Newton::Newton

(

const Newton &

other

)

Copy constructor.

Parameters

other

optimizer to be copied

References fHessian.

~Newton()

sgpp::optimization::optimizer::Newton::~Newton ( )

override

Destructor.

Member Function Documentation

clone()

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

overridevirtual

Parameters

[out]

clone

pointer to cloned object

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

References Newton().

getAlpha1()

double sgpp::optimization::optimizer::Newton::getAlpha1

(

)

const

Returns

steepest descent restart parameter 1

References alpha1.

getAlpha2()

double sgpp::optimization::optimizer::Newton::getAlpha2

(

)

const

Returns

steepest descent restart parameter 2

References alpha2.

getBeta()

double sgpp::optimization::optimizer::Newton::getBeta

(

)

const

Returns

beta (parameter for Armijo's rule)

References beta.

getEpsilon()

double sgpp::optimization::optimizer::Newton::getEpsilon

(

)

const

Returns

epsilon (parameter for Armijo's rule)

References eps.

getGamma()

double sgpp::optimization::optimizer::Newton::getGamma

(

)

const

Returns

gamma (parameter for Armijo's rule)

References gamma.

getObjectiveHessian()

ScalarFunctionHessian & sgpp::optimization::optimizer::Newton::getObjectiveHessian

(

)

const

Returns

objective function Hessian

References fHessian.

getP()

double sgpp::optimization::optimizer::Newton::getP

(

)

const

Returns

steepest descent restart exponent

References p.

getTolerance()

double sgpp::optimization::optimizer::Newton::getTolerance

(

)

const

Returns

tolerance (parameter for Armijo's rule)

References tol.

optimize()

void sgpp::optimization::optimizer::Newton::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 alpha1, alpha2, sgpp::base::DataVector::append(), sgpp::base::DataMatrix::appendRow(), beta, sgpp::optimization::Printer::disableStatusPrinting(), sgpp::base::DataVector::dotProduct(), sgpp::optimization::Printer::enableStatusPrinting(), eps, sgpp::optimization::optimizer::UnconstrainedOptimizer::f, fHessian, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, gamma, sgpp::optimization::Printer::getInstance(), sgpp::optimization::Printer::isStatusPrintingEnabled(), sgpp::base::DataVector::l2Norm(), sgpp::optimization::optimizer::lineSearchArmijo(), sgpp::optimization::optimizer::UnconstrainedOptimizer::N, p, sgpp::combigrid::pow(), sgpp::optimization::Printer::printStatusBegin(), sgpp::optimization::Printer::printStatusEnd(), sgpp::optimization::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), create_scripts::s, sleSolver, sgpp::optimization::sle_solver::SLESolver::solve(), tol, sgpp::base::DataVector::toString(), sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

setAlpha1()

void sgpp::optimization::optimizer::Newton::setAlpha1

(

double

alpha1

)

Parameters

alpha1

steepest descent restart parameter 1

References alpha1.

setAlpha2()

void sgpp::optimization::optimizer::Newton::setAlpha2

(

double

alpha2

)

Parameters

alpha2

steepest descent restart parameter 2

References alpha2.

setBeta()

void sgpp::optimization::optimizer::Newton::setBeta

(

double

beta

)

Parameters

beta	beta (parameter for Armijo's rule)

References beta.

setEpsilon()

void sgpp::optimization::optimizer::Newton::setEpsilon

(

double

epsilon

)

Parameters

epsilon

epsilon (parameter for Armijo's rule)

References eps.

setGamma()

void sgpp::optimization::optimizer::Newton::setGamma

(

double

gamma

)

Parameters

gamma

gamma (parameter for Armijo's rule)

References gamma.

setP()

void sgpp::optimization::optimizer::Newton::setP

(

double

p

)

Parameters

p	steepest descent restart exponent

References p.

setTolerance()

void sgpp::optimization::optimizer::Newton::setTolerance

(

double

tolerance

)

Parameters

tolerance

tolerance (parameter for Armijo's rule)

References tol.

Member Data Documentation

alpha1

double sgpp::optimization::optimizer::Newton::alpha1

protected

steepest descent restart parameter 1

Referenced by getAlpha1(), optimize(), and setAlpha1().

alpha2

double sgpp::optimization::optimizer::Newton::alpha2

protected

steepest descent restart parameter 2

Referenced by getAlpha2(), optimize(), and setAlpha2().

beta

double sgpp::optimization::optimizer::Newton::beta

protected

beta (parameter for Armijo's rule)

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

DEFAULT_ALPHA1

constexpr double sgpp::optimization::optimizer::Newton::DEFAULT_ALPHA1 = 1e-6

static

default steepest descent restart parameter 1

DEFAULT_ALPHA2

constexpr double sgpp::optimization::optimizer::Newton::DEFAULT_ALPHA2 = 1e-6

static

default steepest descent restart parameter 2

DEFAULT_BETA

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

static

default beta (parameter for Armijo's rule)

DEFAULT_EPSILON

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

static

default epsilon (parameter for Armijo's rule)

DEFAULT_GAMMA

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

static

default gamma (parameter for Armijo's rule)

DEFAULT_P

constexpr double sgpp::optimization::optimizer::Newton::DEFAULT_P = 0.1

static

default steepest descent restart exponent

DEFAULT_TOLERANCE

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

static

default tolerance (parameter for Armijo's rule)

defaultSleSolver

const sle_solver::GaussianElimination sgpp::optimization::optimizer::Newton::defaultSleSolver

protected

default linear solver

eps

double sgpp::optimization::optimizer::Newton::eps

protected

epsilon (parameter for Armijo's rule)

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

fHessian

std::unique_ptr<ScalarFunctionHessian> sgpp::optimization::optimizer::Newton::fHessian

protected

objective function Hessian

Referenced by getObjectiveHessian(), Newton(), and optimize().

gamma

double sgpp::optimization::optimizer::Newton::gamma

protected

gamma (parameter for Armijo's rule)

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

p

double sgpp::optimization::optimizer::Newton::p

protected

steepest descent restart exponent

Referenced by getP(), optimize(), and setP().

sleSolver

const sle_solver::SLESolver& sgpp::optimization::optimizer::Newton::sleSolver

protected

linear solver

Referenced by optimize().

tol

double sgpp::optimization::optimizer::Newton::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/Newton.hpp
• optimization/src/sgpp/optimization/optimizer/unconstrained/Newton.cpp