Augmented Lagrangian method for constrained optimization. More...

#include <AugmentedLagrangian.hpp>

Inheritance diagram for sgpp::optimization::optimizer::AugmentedLagrangian:

Public Member Functions
	AugmentedLagrangian (const ScalarFunction &f, const ScalarFunctionGradient &fGradient, const VectorFunction &g, const VectorFunctionGradient &gGradient, const VectorFunction &h, const VectorFunctionGradient &hGradient, size_t maxItCount=DEFAULT_N, double xTolerance=DEFAULT_X_TOLERANCE, double constraintTolerance=DEFAULT_CONSTRAINT_TOLERANCE, double penaltyStartValue=DEFAULT_PENALTY_START_VALUE, double penaltyIncreaseFactor=DEFAULT_PENALTY_INCREASE_FACTOR)
	Constructor. More...

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

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

base::DataVector	findFeasiblePoint () const
	Try to find a feasible initial point by solving an auxiliary problem. More...

double	getConstraintTolerance () const

VectorFunctionGradient &	getEqualityConstraintGradient () const

const std::vector< size_t > &	getHistoryOfInnerIterationNumbers () const

const base::DataMatrix &	getHistoryOfInnerIterationPoints () const

VectorFunctionGradient &	getInequalityConstraintGradient () const

ScalarFunctionGradient &	getObjectiveGradient () const

double	getPenaltyIncreaseFactor () const

double	getPenaltyStartValue () const

double	getXTolerance () const

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

void	setConstraintTolerance (double constraintTolerance)

void	setPenaltyIncreaseFactor (double penaltyIncreaseFactor)

void	setPenaltyStartValue (double penaltyStartValue)

void	setXTolerance (double xTolerance)

	~AugmentedLagrangian () override
	Destructor. More...

Public Member Functions inherited from sgpp::optimization::optimizer::ConstrainedOptimizer
	ConstrainedOptimizer (const ScalarFunction &f, const VectorFunction &g, const VectorFunction &h, size_t N=DEFAULT_N)
	Constructor. More...

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

VectorFunction &	getEqualityConstraintFunction () const

VectorFunction &	getInequalityConstraintFunction () const

	~ConstrainedOptimizer () 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_CONSTRAINT_TOLERANCE = 1e-6
	default constraint tolerance More...

static constexpr double	DEFAULT_PENALTY_INCREASE_FACTOR = 1.0
	default penalty increase factor More...

static constexpr double	DEFAULT_PENALTY_START_VALUE = 1.0
	default penalty start value More...

static constexpr double	DEFAULT_X_TOLERANCE = 1e-6
	default point tolerance 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	epsilon
	constraint tolerance More...

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

std::unique_ptr< VectorFunctionGradient >	gGradient
	inequality constraint function gradient More...

std::unique_ptr< VectorFunctionGradient >	hGradient
	equality constraint function gradient More...

std::vector< size_t >	kHistInner
	search history (number of inner iterations) More...

double	mu0
	penalty start value More...

double	rhoMuPlus
	penalty increase factor More...

double	theta
	point tolerance More...

base::DataMatrix	xHistInner
	search history (inner iterations) More...

Protected Attributes inherited from sgpp::optimization::optimizer::ConstrainedOptimizer
std::unique_ptr< VectorFunction >	g
	inequality constraint function More...

std::unique_ptr< VectorFunction >	h
	equality constraint function 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

Augmented Lagrangian method for constrained optimization.

Constructor & Destructor Documentation

◆ AugmentedLagrangian() [1/2]

sgpp::optimization::optimizer::AugmentedLagrangian::AugmentedLagrangian	(	const ScalarFunction &	f,
		const ScalarFunctionGradient &	fGradient,
		const VectorFunction &	g,
		const VectorFunctionGradient &	gGradient,
		const VectorFunction &	h,
		const VectorFunctionGradient &	hGradient,
		size_t	maxItCount = `DEFAULT_N`,
		double	xTolerance = `DEFAULT_X_TOLERANCE`,
		double	constraintTolerance = `DEFAULT_CONSTRAINT_TOLERANCE`,
		double	penaltyStartValue = `DEFAULT_PENALTY_START_VALUE`,
		double	penaltyIncreaseFactor = `DEFAULT_PENALTY_INCREASE_FACTOR`
	)

Constructor.

Parameters

f	objective function
fGradient	objective function gradient
g	inequality constraint
gGradient	inequality constraint gradient
h	equality constraint
hGradient	equality constraint gradient
maxItCount	maximal number of function evaluations
xTolerance	point tolerance
constraintTolerance	constraint tolerance
penaltyStartValue	penalty start value
penaltyIncreaseFactor	penalty increase factor

References sgpp::optimization::ScalarFunctionGradient::clone(), and sgpp::optimization::VectorFunctionGradient::clone().

Referenced by clone().

◆ AugmentedLagrangian() [2/2]

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

Copy constructor.

Parameters

other optimizer to be copied

References fGradient, gGradient, and hGradient.

◆ ~AugmentedLagrangian()

sgpp::optimization::optimizer::AugmentedLagrangian::~AugmentedLagrangian ( )

override

Destructor.

Member Function Documentation

◆ clone()

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

overridevirtual

Parameters

[out] clone pointer to cloned object

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

References AugmentedLagrangian().

◆ findFeasiblePoint()

base::DataVector sgpp::optimization::optimizer::AugmentedLagrangian::findFeasiblePoint ( ) const

Try to find a feasible initial point by solving an auxiliary problem.

However, it is not guaranteed that the method works, i.e., it should be checked afterwards that the returned point is actually feasible.

Returns: feasible point in \([0, 1]^d\)

References sgpp::optimization::optimizer::UnconstrainedOptimizer::f, sgpp::optimization::optimizer::ConstrainedOptimizer::g, sgpp::optimization::EmptyVectorFunction::getInstance(), sgpp::optimization::EmptyVectorFunctionGradient::getInstance(), sgpp::optimization::optimizer::UnconstrainedOptimizer::getOptimalPoint(), gGradient, sgpp::optimization::optimizer::ConstrainedOptimizer::h, hGradient, sgpp::base::DataVector::max(), sgpp::base::DataVector::maxNorm(), mG, mH, optimize(), sgpp::optimization::optimizer::UnconstrainedOptimizer::setStartingPoint(), sMax, and sMin.

◆ getConstraintTolerance()

double sgpp::optimization::optimizer::AugmentedLagrangian::getConstraintTolerance ( ) const

Returns: constraint tolerance

References epsilon.

◆ getEqualityConstraintGradient()

VectorFunctionGradient & sgpp::optimization::optimizer::AugmentedLagrangian::getEqualityConstraintGradient ( ) const

Returns: equality constraint function gradient

References hGradient.

◆ getHistoryOfInnerIterationNumbers()

const std::vector< size_t > & sgpp::optimization::optimizer::AugmentedLagrangian::getHistoryOfInnerIterationNumbers ( ) const

Returns: vector in which the k-th entry indicates the number of inner iterations in the k-th (outer) iteration, empty vector on error

References kHistInner.

◆ getHistoryOfInnerIterationPoints()

const base::DataMatrix & sgpp::optimization::optimizer::AugmentedLagrangian::getHistoryOfInnerIterationPoints ( ) const

Returns: tall matrix (d columns) in which the history of optimal points of the iterations are concatenated

References xHistInner.

◆ getInequalityConstraintGradient()

VectorFunctionGradient & sgpp::optimization::optimizer::AugmentedLagrangian::getInequalityConstraintGradient ( ) const

Returns: inequality constraint function gradient

References gGradient.

◆ getObjectiveGradient()

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

Returns: objective function gradient

References fGradient.

◆ getPenaltyIncreaseFactor()

double sgpp::optimization::optimizer::AugmentedLagrangian::getPenaltyIncreaseFactor ( ) const

Returns: penalty increase factor

References rhoMuPlus.

◆ getPenaltyStartValue()

double sgpp::optimization::optimizer::AugmentedLagrangian::getPenaltyStartValue ( ) const

Returns: penalty start value

References mu0.

◆ getXTolerance()

double sgpp::optimization::optimizer::AugmentedLagrangian::getXTolerance ( ) const

Returns: point tolerance

References theta.

◆ optimize()

void sgpp::optimization::optimizer::AugmentedLagrangian::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(), epsilon, sgpp::optimization::optimizer::UnconstrainedOptimizer::f, fGradient, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, sgpp::optimization::optimizer::ConstrainedOptimizer::g, sgpp::optimization::optimizer::UnconstrainedOptimizer::getHistoryOfOptimalPoints(), sgpp::optimization::Printer::getInstance(), sgpp::base::DataMatrix::getNrows(), sgpp::optimization::optimizer::UnconstrainedOptimizer::getOptimalPoint(), gGradient, sgpp::optimization::optimizer::ConstrainedOptimizer::h, hGradient, python.statsfileInfo::i, kHistInner, sgpp::base::DataVector::l2Norm(), lambda, sgpp::base::DataVector::max(), sgpp::base::DataVector::maxNorm(), mG, mH, mu, mu0, sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::optimization::optimizer::AdaptiveGradientDescent::optimize(), sgpp::optimization::Printer::printStatusBegin(), sgpp::optimization::Printer::printStatusEnd(), sgpp::optimization::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), rhoMuPlus, sgpp::optimization::optimizer::UnconstrainedOptimizer::setStartingPoint(), sgpp::base::DataVector::sub(), theta, sgpp::base::DataVector::toString(), sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, xHistInner, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

Referenced by findFeasiblePoint().

◆ setConstraintTolerance()

void sgpp::optimization::optimizer::AugmentedLagrangian::setConstraintTolerance ( double constraintTolerance )

Parameters

constraintTolerance constraint tolerance

References epsilon.

◆ setPenaltyIncreaseFactor()

void sgpp::optimization::optimizer::AugmentedLagrangian::setPenaltyIncreaseFactor ( double penaltyIncreaseFactor )

Parameters

penaltyIncreaseFactor penalty increase factor

References rhoMuPlus.

◆ setPenaltyStartValue()

void sgpp::optimization::optimizer::AugmentedLagrangian::setPenaltyStartValue ( double penaltyStartValue )

Parameters

penaltyStartValue penalty start value

References mu0.

◆ setXTolerance()

void sgpp::optimization::optimizer::AugmentedLagrangian::setXTolerance ( double xTolerance )

Parameters

xTolerance point tolerance

References theta.

Member Data Documentation

◆ DEFAULT_CONSTRAINT_TOLERANCE

constexpr double sgpp::optimization::optimizer::AugmentedLagrangian::DEFAULT_CONSTRAINT_TOLERANCE = 1e-6

static

default constraint tolerance

◆ DEFAULT_PENALTY_INCREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AugmentedLagrangian::DEFAULT_PENALTY_INCREASE_FACTOR = 1.0

static

default penalty increase factor

◆ DEFAULT_PENALTY_START_VALUE

constexpr double sgpp::optimization::optimizer::AugmentedLagrangian::DEFAULT_PENALTY_START_VALUE = 1.0

static

default penalty start value

◆ DEFAULT_X_TOLERANCE

constexpr double sgpp::optimization::optimizer::AugmentedLagrangian::DEFAULT_X_TOLERANCE = 1e-6

static

default point tolerance

◆ epsilon

double sgpp::optimization::optimizer::AugmentedLagrangian::epsilon

protected

constraint tolerance

Referenced by getConstraintTolerance(), optimize(), and setConstraintTolerance().

◆ fGradient

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

protected

objective function gradient

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

◆ gGradient

std::unique_ptr<VectorFunctionGradient> sgpp::optimization::optimizer::AugmentedLagrangian::gGradient

protected

inequality constraint function gradient

Referenced by AugmentedLagrangian(), findFeasiblePoint(), getInequalityConstraintGradient(), and optimize().

◆ hGradient

std::unique_ptr<VectorFunctionGradient> sgpp::optimization::optimizer::AugmentedLagrangian::hGradient

protected

equality constraint function gradient

Referenced by AugmentedLagrangian(), findFeasiblePoint(), getEqualityConstraintGradient(), and optimize().

◆ kHistInner

std::vector<size_t> sgpp::optimization::optimizer::AugmentedLagrangian::kHistInner

protected

search history (number of inner iterations)

Referenced by getHistoryOfInnerIterationNumbers(), and optimize().

◆ mu0

double sgpp::optimization::optimizer::AugmentedLagrangian::mu0

protected

penalty start value

Referenced by getPenaltyStartValue(), optimize(), and setPenaltyStartValue().

◆ rhoMuPlus

double sgpp::optimization::optimizer::AugmentedLagrangian::rhoMuPlus

protected

penalty increase factor

Referenced by getPenaltyIncreaseFactor(), optimize(), and setPenaltyIncreaseFactor().

◆ theta

double sgpp::optimization::optimizer::AugmentedLagrangian::theta

protected

point tolerance

Referenced by getXTolerance(), optimize(), and setXTolerance().

◆ xHistInner

base::DataMatrix sgpp::optimization::optimizer::AugmentedLagrangian::xHistInner

protected

search history (inner iterations)

Referenced by getHistoryOfInnerIterationPoints(), and optimize().

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

optimization/src/sgpp/optimization/optimizer/constrained/AugmentedLagrangian.hpp
optimization/src/sgpp/optimization/optimizer/constrained/AugmentedLagrangian.cpp

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ AugmentedLagrangian() [1/2]

◆ AugmentedLagrangian() [2/2]

◆ ~AugmentedLagrangian()

Member Function Documentation

◆ clone()

◆ findFeasiblePoint()

◆ getConstraintTolerance()

◆ getEqualityConstraintGradient()

◆ getHistoryOfInnerIterationNumbers()

◆ getHistoryOfInnerIterationPoints()

◆ getInequalityConstraintGradient()

◆ getObjectiveGradient()

◆ getPenaltyIncreaseFactor()

◆ getPenaltyStartValue()

◆ getXTolerance()

◆ optimize()

◆ setConstraintTolerance()

◆ setPenaltyIncreaseFactor()

◆ setPenaltyStartValue()

◆ setXTolerance()

Member Data Documentation

◆ DEFAULT_CONSTRAINT_TOLERANCE

◆ DEFAULT_PENALTY_INCREASE_FACTOR

◆ DEFAULT_PENALTY_START_VALUE

◆ DEFAULT_X_TOLERANCE

◆ epsilon

◆ fGradient

◆ gGradient

◆ hGradient

◆ kHistInner

◆ mu0

◆ rhoMuPlus

◆ theta

◆ xHistInner