Implements the Augmented Lagrangian optimization method of Birgin & Martinez. More...

#include <AugmentedLagrangianOptimizer.h>

Public Types
using	ObjFunction = boost::function< double(const size_t, const double *)>
	Function type. More...

Public Member Functions
	AugmentedLagrangianOptimizer ()=delete
	Disable default constructor. More...

	AugmentedLagrangianOptimizer (const AugmentedLagrangianOptimizer &)=delete
	Disable copy operator. More...

	AugmentedLagrangianOptimizer (const size_t nparams, const ObjFunction &objfunc)
	Constructor. More...

	AugmentedLagrangianOptimizer (const size_t nparams, const ObjFunction &objfunc, const Kernel::DblMatrix &equality, const Kernel::DblMatrix &inequality)
	Constructor with constraints. More...

void	minimize (std::vector< double > &xv) const
	Perform the minimization. More...

size_t	numEqualityConstraints () const

size_t	numInequalityConstraints () const

size_t	numParameters () const

AugmentedLagrangianOptimizer &	operator= (const AugmentedLagrangianOptimizer &)=delete
	Disable assignment operator. More...

void	setMaxIterations (const int maxIter)
	Override the maximum number of iterations (Default = 500) More...

Private Member Functions
void	checkConstraints (const Kernel::DblMatrix &equality, const Kernel::DblMatrix &inequality)
	Sanity check for constraint inputs. More...

void	unconstrainedOptimization (const std::vector< double > &lambda, const std::vector< double > &mu, const double rho, std::vector< double > &xcur) const
	Using gradient optimizer to perform limited optimization of current set. More...

Private Attributes
Kernel::DblMatrix	m_eq
	Defines the equality constraints. More...

Kernel::DblMatrix	m_ineq
	Defines the inequality constraints. More...

int	m_maxIter
	Maximum number of iterations. More...

const size_t	m_neq
	Number of equality constraints. More...

const size_t	m_nineq
	Number of inequality constraints. More...

const size_t	m_nparams
	Number of parameters under minimization. More...

ObjFunction	m_userfunc
	User-defined function. More...

Friends
class	UnconstrainedCostFunction

Detailed Description

Implements the Augmented Lagrangian optimization method of Birgin & Martinez.

See

E. G. Birgin and J. M. Martiinez, "Improving ultimate convergence of an augmented Lagrangian method,", Optimization Methods and Software vol. 23, no. 2, p. 177-195 (2008).

If the objective function is written as

\[ Cx = d \]

where \(x\) are the parameters, then the routine attempts to minimize

\[ \frac{1}{2}||Cx - d||^2 \]

where \( ||f|| \) denotes the 2nd-norm of \(f\). It possible to specify an optional set of constraints such that the function is minimized subject to

\[ Ax \geq 0 \]

and

\[ A_{eq} x = 0 \]

Definition at line 53 of file AugmentedLagrangianOptimizer.h.

Member Typedef Documentation

◆ ObjFunction

using Mantid::CurveFitting::AugmentedLagrangianOptimizer::ObjFunction = boost::function<double(const size_t, const double *)>

Function type.

Definition at line 57 of file AugmentedLagrangianOptimizer.h.

Constructor & Destructor Documentation

◆ AugmentedLagrangianOptimizer() [1/4]

Mantid::CurveFitting::AugmentedLagrangianOptimizer::AugmentedLagrangianOptimizer	(	const size_t	nparams,
		const ObjFunction &	objfunc
	)

inline

Constructor.

Parameters

nparams	The number of parameters in the problem
objfunc	An object whose type has a member named eval with the following signature "double eval(const std::vector<double> &) const" to return the value of the objective function at a given pt

Definition at line 69 of file AugmentedLagrangianOptimizer.h.

◆ AugmentedLagrangianOptimizer() [2/4]

Mantid::CurveFitting::AugmentedLagrangianOptimizer::AugmentedLagrangianOptimizer	(	const size_t	nparams,
		const ObjFunction &	objfunc,
		const Kernel::DblMatrix &	equality,
		const Kernel::DblMatrix &	inequality
	)

inline

Constructor with constraints.

Parameters

nparams	The number of parameters in the problem
objfunc	An object whose type has a member named eval with the following signature "double eval(const std::vector<double> &)" to return the value of the objective function at a given pt
equality	A matrix of coefficients, \(A_{eq}\) such that in the final solution \(A_{eq} x = 0\)
inequality	A matrix of coefficients, \(A\) such that in the final solution \(A_{eq} x\geq 0\)

Definition at line 85 of file AugmentedLagrangianOptimizer.h.

◆ AugmentedLagrangianOptimizer() [3/4]

Mantid::CurveFitting::AugmentedLagrangianOptimizer::AugmentedLagrangianOptimizer ( )

delete

Disable default constructor.

◆ AugmentedLagrangianOptimizer() [4/4]

Mantid::CurveFitting::AugmentedLagrangianOptimizer::AugmentedLagrangianOptimizer ( const AugmentedLagrangianOptimizer & )

delete

Disable copy operator.

Member Function Documentation

◆ checkConstraints()

void Mantid::CurveFitting::AugmentedLagrangianOptimizer::checkConstraints	(	const Kernel::DblMatrix &	equality,
		const Kernel::DblMatrix &	inequality
	)

private

Sanity check for constraint inputs.

Parameters

equality	A matrix of equality constraints \(A_{eq}\)(the number of columns must match number of parameters) where \(A_{eq} x = 0\)
inequality	A matrix of inequality constraints (the number of columns must match number of parameters where \(A_{eq} x \geq 0\)

Definition at line 352 of file AugmentedLagrangianOptimizer.cpp.

References ncols, Mantid::Kernel::Matrix< T >::numCols(), numEqualityConstraints(), numInequalityConstraints(), and numParameters().

◆ minimize()

void Mantid::CurveFitting::AugmentedLagrangianOptimizer::minimize ( std::vector< double > & xv ) const

Perform the minimization.

Perform the minimization using the Augmented Lagrangian routine.

Parameters

xv	The starting parameter values. They will get updated with the values as the routine progresses

Definition at line 130 of file AugmentedLagrangianOptimizer.cpp.

References fabs, Mantid::CurveFitting::FTolReached, lambda, m_eq, m_ineq, m_maxIter, m_userfunc, numEqualityConstraints(), numInequalityConstraints(), numParameters(), rho, Mantid::CurveFitting::Success, unconstrainedOptimization(), and Mantid::CurveFitting::XTolReached.

Referenced by Mantid::CurveFitting::Functions::ComptonScatteringCountRate::iterationStarting().

◆ numEqualityConstraints()

size_t Mantid::CurveFitting::AugmentedLagrangianOptimizer::numEqualityConstraints ( ) const

inline

Returns: The number of equality constraints

Definition at line 104 of file AugmentedLagrangianOptimizer.h.

Referenced by checkConstraints(), and minimize().

◆ numInequalityConstraints()

size_t Mantid::CurveFitting::AugmentedLagrangianOptimizer::numInequalityConstraints ( ) const

inline

Returns: The number of inequality constraints

Definition at line 106 of file AugmentedLagrangianOptimizer.h.

Referenced by checkConstraints(), and minimize().

◆ numParameters()

size_t Mantid::CurveFitting::AugmentedLagrangianOptimizer::numParameters ( ) const

inline

Returns: The number of parameters under minimization

Definition at line 102 of file AugmentedLagrangianOptimizer.h.

Referenced by checkConstraints(), minimize(), and unconstrainedOptimization().

◆ operator=()

AugmentedLagrangianOptimizer & Mantid::CurveFitting::AugmentedLagrangianOptimizer::operator= ( const AugmentedLagrangianOptimizer & )

delete

Disable assignment operator.

◆ setMaxIterations()

void Mantid::CurveFitting::AugmentedLagrangianOptimizer::setMaxIterations ( const int maxIter )

inline

Override the maximum number of iterations (Default = 500)

Parameters

maxIter Maximum value for the main minimizer loop

Definition at line 112 of file AugmentedLagrangianOptimizer.h.

◆ unconstrainedOptimization()

void Mantid::CurveFitting::AugmentedLagrangianOptimizer::unconstrainedOptimization	(	const std::vector< double > &	lambda,
		const std::vector< double > &	mu,
		const double	rho,
		std::vector< double > &	xcur
	)		const