sgpp::optimization::optimizer::NelderMead Class Reference

Gradient-free Nelder-Mead method. More...

#include <NelderMead.hpp>

Inheritance diagram for sgpp::optimization::optimizer::NelderMead:

Public Member Functions
void	clone (std::unique_ptr< UnconstrainedOptimizer > &clone) const override
double	getAlpha () const
double	getBeta () const
double	getDelta () const
double	getGamma () const
	NelderMead (const base::ScalarFunction &f, size_t maxFcnEvalCount=DEFAULT_MAX_FCN_EVAL_COUNT, double alpha=DEFAULT_ALPHA, double beta=DEFAULT_BETA, double gamma=DEFAULT_GAMMA, double delta=DEFAULT_DELTA)
	Constructor.
	NelderMead (const NelderMead &other)
	Copy constructor.
void	optimize () override
	Pure virtual method for optimization of the objective function.
void	setAlpha (double alpha)
void	setBeta (double beta)
void	setDelta (double delta)
void	setGamma (double gamma)
	~NelderMead () 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_ALPHA = 1.0
	default reflection coefficient
static constexpr double	DEFAULT_BETA = 2.0
	default expansion coefficient
static constexpr double	DEFAULT_DELTA = 0.5
	default shrinking coefficient
static constexpr double	DEFAULT_GAMMA = 0.5
	default contraction coefficient
static const size_t	DEFAULT_MAX_FCN_EVAL_COUNT = 1000
	default maximal number of function evaluations
static constexpr double	STARTING_SIMPLEX_EDGE_LENGTH = 0.4
	edge length of starting simplex
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
	reflection coefficient
double	beta
	expansion coefficient
double	delta
	shrinking coefficient
double	gamma
	contraction coefficient
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-free Nelder-Mead method.

Constructor & Destructor Documentation

NelderMead() [1/2]

sgpp::optimization::optimizer::NelderMead::NelderMead	(	const base::ScalarFunction &	f,
		size_t	maxFcnEvalCount = DEFAULT_MAX_FCN_EVAL_COUNT,
		double	alpha = DEFAULT_ALPHA,
		double	beta = DEFAULT_BETA,
		double	gamma = DEFAULT_GAMMA,
		double	delta = DEFAULT_DELTA
	)

Constructor.

The starting point is set to \((0.5, \dotsc, 0.5)^{\mathrm{T}}\).

Parameters

f	objective function
maxFcnEvalCount	maximal number of function evaluations
alpha	reflection coefficient
beta	expansion coefficient
gamma	contraction coefficient
delta	shrinking coefficient

NelderMead() [2/2]

sgpp::optimization::optimizer::NelderMead::NelderMead

(

const NelderMead &

other

)

Copy constructor.

Parameters

other

optimizer to be copied

~NelderMead()

sgpp::optimization::optimizer::NelderMead::~NelderMead ( )

override

Destructor.

Member Function Documentation

clone()

void sgpp::optimization::optimizer::NelderMead::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(), and sgpp::optimization::optimizer::MultiStart::MultiStart().

getAlpha()

double sgpp::optimization::optimizer::NelderMead::getAlpha

(

)

const

Returns

reflection coefficient

References alpha.

Referenced by python.uq.analysis.asgc.ASGCKnowledge.ASGCKnowledge::getSparseGridFunction().

getBeta()

double sgpp::optimization::optimizer::NelderMead::getBeta

(

)

const

Returns

expansion coefficient

References beta.

getDelta()

double sgpp::optimization::optimizer::NelderMead::getDelta

(

)

const

Returns

shrinking coefficient

References delta.

getGamma()

double sgpp::optimization::optimizer::NelderMead::getGamma

(

)

const

Returns

contraction coefficient

References gamma.

optimize()

void sgpp::optimization::optimizer::NelderMead::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, delta, sgpp::optimization::optimizer::UnconstrainedOptimizer::f, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, gamma, sgpp::base::Printer::getInstance(), sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::base::Printer::printStatusBegin(), sgpp::base::Printer::printStatusEnd(), sgpp::base::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), STARTING_SIMPLEX_EDGE_LENGTH, sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

Referenced by sgpp::datadriven::OperationInverseRosenblattTransformation1DBspline::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DBsplineBoundary::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DBsplineClenshawCurtis::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DModBspline::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DModBsplineClenshawCurtis::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DModPoly::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DModPolyClenshawCurtis::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DPoly::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DPolyBoundary::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DPolyClenshawCurtis::doTransformation1D(), sgpp::datadriven::OperationInverseRosenblattTransformation1DPolyClenshawCurtisBoundary::doTransformation1D(), and sgpp::datadriven::MaximumLikelihoodCrossValidation::optimizeBandwidths().

setAlpha()

void sgpp::optimization::optimizer::NelderMead::setAlpha

(

double

alpha

)

Parameters

alpha

reflection coefficient

References alpha.

setBeta()

void sgpp::optimization::optimizer::NelderMead::setBeta

(

double

beta

)

Parameters

beta	expansion coefficient

References beta.

setDelta()

void sgpp::optimization::optimizer::NelderMead::setDelta

(

double

delta

)

Parameters

delta

shrinking coefficient

References delta.

setGamma()

void sgpp::optimization::optimizer::NelderMead::setGamma

(

double

gamma

)

Parameters

gamma

contraction coefficient

References gamma.

Member Data Documentation

alpha

double sgpp::optimization::optimizer::NelderMead::alpha

protected

reflection coefficient

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

beta

double sgpp::optimization::optimizer::NelderMead::beta

protected

expansion coefficient

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

DEFAULT_ALPHA

constexpr double sgpp::optimization::optimizer::NelderMead::DEFAULT_ALPHA = 1.0

staticconstexpr

default reflection coefficient

DEFAULT_BETA

constexpr double sgpp::optimization::optimizer::NelderMead::DEFAULT_BETA = 2.0

staticconstexpr

default expansion coefficient

DEFAULT_DELTA

constexpr double sgpp::optimization::optimizer::NelderMead::DEFAULT_DELTA = 0.5

staticconstexpr

default shrinking coefficient

DEFAULT_GAMMA

constexpr double sgpp::optimization::optimizer::NelderMead::DEFAULT_GAMMA = 0.5

staticconstexpr

default contraction coefficient

DEFAULT_MAX_FCN_EVAL_COUNT

const size_t sgpp::optimization::optimizer::NelderMead::DEFAULT_MAX_FCN_EVAL_COUNT = 1000

static

default maximal number of function evaluations

delta

double sgpp::optimization::optimizer::NelderMead::delta

protected

shrinking coefficient

Referenced by getDelta(), optimize(), and setDelta().

gamma

double sgpp::optimization::optimizer::NelderMead::gamma

protected

contraction coefficient

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

STARTING_SIMPLEX_EDGE_LENGTH

constexpr double sgpp::optimization::optimizer::NelderMead::STARTING_SIMPLEX_EDGE_LENGTH = 0.4

staticconstexpr

edge length of starting simplex

Referenced by optimize().

---

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

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