sgpp::optimization::optimizer::AugmentedLagrangian Class Reference

Augmented Lagrangian method for constrained optimization. More...

#include <AugmentedLagrangian.hpp>

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

Public Member Functions
	AugmentedLagrangian (const AugmentedLagrangian &other)
	Copy constructor.
	AugmentedLagrangian (const base::ScalarFunction &f, const base::ScalarFunctionGradient &fGradient, const base::VectorFunction &g, const base::VectorFunctionGradient &gGradient, const base::VectorFunction &h, const base::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 with adaptive gradient descent as optimization algorithm (gradient-based).
	AugmentedLagrangian (const base::ScalarFunction &f, const base::VectorFunction &g, const base::VectorFunction &h, 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 with Nelder-Mead as optimization algorithm (gradient-free).
	AugmentedLagrangian (const UnconstrainedOptimizer &unconstrainedOptimizer, const base::VectorFunction &g, const base::VectorFunctionGradient *gGradient, const base::VectorFunction &h, const base::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 with custom unconstrained optimization algorithm (gradient-free or gradient-based).
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.
double	getConstraintTolerance () const
const std::vector< size_t > &	getHistoryOfInnerIterationNumbers () const
const base::DataMatrix &	getHistoryOfInnerIterationPoints () const
double	getPenaltyIncreaseFactor () const
double	getPenaltyStartValue () const
double	getXTolerance () const
void	optimize () override
	Pure virtual method for optimization of the objective function.
void	setConstraintTolerance (double constraintTolerance)
void	setPenaltyIncreaseFactor (double penaltyIncreaseFactor)
void	setPenaltyStartValue (double penaltyStartValue)
void	setXTolerance (double xTolerance)
	~AugmentedLagrangian () override
	Destructor.
Public Member Functions inherited from sgpp::optimization::optimizer::ConstrainedOptimizer
	ConstrainedOptimizer (const base::ScalarFunction &f, const base::ScalarFunctionGradient &fGradient, const base::VectorFunction &g, const base::VectorFunctionGradient &gGradient, const base::VectorFunction &h, const base::VectorFunctionGradient &hGradient, size_t N=DEFAULT_N)
	Constructor.
	ConstrainedOptimizer (const base::ScalarFunction &f, const base::VectorFunction &g, const base::VectorFunction &h, size_t N=DEFAULT_N)
	Constructor.
	ConstrainedOptimizer (const ConstrainedOptimizer &other)
	Copy constructor.
	ConstrainedOptimizer (const UnconstrainedOptimizer &unconstrainedOptimizer, const base::VectorFunction &g, const base::VectorFunctionGradient *gGradient, const base::VectorFunction &h, const base::VectorFunctionGradient *hGradient, size_t N=DEFAULT_N)
	Constructor with custom unconstrained optimization algorithm (gradient-free or gradient-based).
base::VectorFunction &	getEqualityConstraintFunction () const
base::VectorFunctionGradient *	getEqualityConstraintGradient () const
base::VectorFunction &	getInequalityConstraintFunction () const
base::VectorFunctionGradient *	getInequalityConstraintGradient () const
void	setEqualityConstraintFunction (const base::VectorFunction &h)
void	setEqualityConstraintGradient (const base::VectorFunctionGradient *hGradient)
void	setInequalityConstraintFunction (const base::VectorFunction &g)
void	setInequalityConstraintGradient (const base::VectorFunctionGradient *gGradient)
	~ConstrainedOptimizer () 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_CONSTRAINT_TOLERANCE = 1e-6
	default constraint tolerance
static constexpr double	DEFAULT_PENALTY_INCREASE_FACTOR = 1.5
	default penalty increase factor
static constexpr double	DEFAULT_PENALTY_START_VALUE = 1.0
	default penalty start value
static constexpr double	DEFAULT_X_TOLERANCE = 1e-6
	default point tolerance
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	epsilon
	constraint tolerance
std::vector< size_t >	kHistInner
	search history (number of inner iterations)
double	mu0
	penalty start value
double	rhoMuPlus
	penalty increase factor
double	theta
	point tolerance
base::DataMatrix	xHistInner
	search history (inner iterations)
Protected Attributes inherited from sgpp::optimization::optimizer::ConstrainedOptimizer
std::unique_ptr< base::VectorFunction >	g
	inequality constraint function
std::unique_ptr< base::VectorFunctionGradient >	gGradient
	inequality constraint function gradient
std::unique_ptr< base::VectorFunction >	h
	equality constraint function
std::unique_ptr< base::VectorFunctionGradient >	hGradient
	equality constraint function gradient
std::unique_ptr< UnconstrainedOptimizer >	unconstrainedOptimizer
	unconstrained optimization algorithm
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

Augmented Lagrangian method for constrained optimization.

Constructor & Destructor Documentation

AugmentedLagrangian() [1/4]

sgpp::optimization::optimizer::AugmentedLagrangian::AugmentedLagrangian	(	const base::ScalarFunction &	f,
		const base::VectorFunction &	g,
		const base::VectorFunction &	h,
		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 with Nelder-Mead as optimization algorithm (gradient-free).

Parameters

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

AugmentedLagrangian() [2/4]

sgpp::optimization::optimizer::AugmentedLagrangian::AugmentedLagrangian	(	const base::ScalarFunction &	f,
		const base::ScalarFunctionGradient &	fGradient,
		const base::VectorFunction &	g,
		const base::VectorFunctionGradient &	gGradient,
		const base::VectorFunction &	h,
		const base::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 with adaptive gradient descent as optimization algorithm (gradient-based).

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 theta, and sgpp::optimization::optimizer::ConstrainedOptimizer::unconstrainedOptimizer.

AugmentedLagrangian() [3/4]

sgpp::optimization::optimizer::AugmentedLagrangian::AugmentedLagrangian	(	const UnconstrainedOptimizer &	unconstrainedOptimizer,
		const base::VectorFunction &	g,
		const base::VectorFunctionGradient *	gGradient,
		const base::VectorFunction &	h,
		const base::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 with custom unconstrained optimization algorithm (gradient-free or gradient-based).

Parameters

unconstrainedOptimizer	unconstrained optimization algorithm
g	inequality constraint
gGradient	inequality constraint gradient (nullptr to omit)
h	equality constraint
hGradient	equality constraint gradient (nullptr to omit)
maxItCount	maximal number of function evaluations
xTolerance	point tolerance
constraintTolerance	constraint tolerance
penaltyStartValue	penalty start value
penaltyIncreaseFactor	penalty increase factor

AugmentedLagrangian() [4/4]

sgpp::optimization::optimizer::AugmentedLagrangian::AugmentedLagrangian

(

const AugmentedLagrangian &

other

)

Copy constructor.

Parameters

other

optimizer to be copied

~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 clone().

Referenced by clone().

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::base::EmptyVectorFunction::getInstance(), sgpp::base::EmptyVectorFunctionGradient::getInstance(), sgpp::optimization::optimizer::ConstrainedOptimizer::gGradient, sgpp::optimization::optimizer::ConstrainedOptimizer::h, sgpp::optimization::optimizer::ConstrainedOptimizer::hGradient, sgpp::base::DataVector::max(), sgpp::base::DataVector::maxNorm(), mG, mH, sMax, and sMin.

getConstraintTolerance()

double sgpp::optimization::optimizer::AugmentedLagrangian::getConstraintTolerance

(

)

const

Returns

constraint tolerance

References epsilon.

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.

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, sgpp::optimization::optimizer::UnconstrainedOptimizer::fGradient, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, sgpp::optimization::optimizer::ConstrainedOptimizer::g, sgpp::base::Printer::getInstance(), sgpp::base::DataMatrix::getNrows(), sgpp::optimization::optimizer::ConstrainedOptimizer::gGradient, sgpp::optimization::optimizer::ConstrainedOptimizer::h, sgpp::optimization::optimizer::ConstrainedOptimizer::hGradient, kHistInner, sgpp::base::DataVector::l2Norm(), lambda, sgpp::base::DataVector::max(), sgpp::base::DataVector::maxNorm(), mG, mH, mu, mu0, sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::base::Printer::printStatusBegin(), sgpp::base::Printer::printStatusEnd(), sgpp::base::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), rhoMuPlus, sgpp::base::DataVector::sub(), theta, sgpp::base::DataVector::toString(), sgpp::optimization::optimizer::ConstrainedOptimizer::unconstrainedOptimizer, sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, xHistInner, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

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

staticconstexpr

default constraint tolerance

DEFAULT_PENALTY_INCREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AugmentedLagrangian::DEFAULT_PENALTY_INCREASE_FACTOR = 1.5

staticconstexpr

default penalty increase factor

DEFAULT_PENALTY_START_VALUE

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

staticconstexpr

default penalty start value

DEFAULT_X_TOLERANCE

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

staticconstexpr

default point tolerance

epsilon

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

protected

constraint tolerance

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

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 AugmentedLagrangian(), 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