Provides the implementation of the buffered probability of exceedance. More...

#include <ROL_BPOE.hpp>

Inheritance diagram for ROL::BPOE< Real >:

Public Member Functions
	BPOE (const Real threshold, const Real order=1)

	BPOE (ROL::ParameterList &parlist)

void	initialize (const Vector< Real > &x)
	Initialize temporary variables. More...

void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
	Update internal storage for value computation. More...

Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
	Return risk measure value. More...

void	updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
	Update internal risk measure storage for gradient computation. More...

void	getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
	Return risk measure (sub)gradient. More...

void	updateHessVec (Objective< Real > &obj, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
	Update internal risk measure storage for Hessian-time-a-vector computation. More...

void	getHessVec (Vector< Real > &hv, std::vector< Real > &hvstat, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
	Return risk measure Hessian-times-a-vector. More...

Public Member Functions inherited from ROL::RandVarFunctional< Real >
virtual	~RandVarFunctional ()

	RandVarFunctional (void)

	weight_ (0)

void	useStorage (bool storage)

void	useHessVecStorage (bool storage)

virtual void	setStorage (const Ptr< SampledScalar< Real >> &value_storage, const Ptr< SampledVector< Real >> &gradient_storage)

virtual void	setHessVecStorage (const Ptr< SampledScalar< Real >> &gradvec_storage, const Ptr< SampledVector< Real >> &hessvec_storage)

virtual void	resetStorage (bool flag=true)
	Reset internal storage. More...

virtual void	setSample (const std::vector< Real > &point, const Real weight)

virtual Real	computeStatistic (const Ptr< const std::vector< Real >> &xstat) const
	Compute statistic. More...

Private Attributes
Real	threshold_

Real	order_

std::vector< Real >	hvec_

ROL::Ptr< Vector< Real > >	dualVec1_

ROL::Ptr< Vector< Real > >	dualVec2_

bool	firstResetBPOE_

Additional Inherited Members
Protected Member Functions inherited from ROL::RandVarFunctional< Real >
Real	computeValue (Objective< Real > &obj, const Vector< Real > &x, Real &tol)

void	computeGradient (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &x, Real &tol)

Real	computeGradVec (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol)

void	computeHessVec (Vector< Real > &hv, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol)

Protected Attributes inherited from ROL::RandVarFunctional< Real >
Real	val_

Real	gv_

Ptr< Vector< Real > >	g_

Ptr< Vector< Real > >	hv_

Ptr< Vector< Real > >	dualVector_

bool	firstReset_

std::vector< Real >	point_

Real	weight_

Detailed Description

template<class Real>
class ROL::BPOE< Real >

Provides the implementation of the buffered probability of exceedance.

Let \((\Omega,\mathcal{F},\mathbb{P})\) be a complete space. Here, \(\Omega\) is the set of outcomes, \(\mathcal{F}\subseteq 2^\Omega\) is a \(\sigma\)-algebra of events and \(\mathbb{P}:\mathcal{F}\to[0,1]\) is a probability measure. Moreover, let \(\mathcal{X}\) be a class of random variables.

ROL's BPOE class inherits from ROL::RandVarFunctional which is written in a way to exploit parallel sampling.

Definition at line 66 of file ROL_BPOE.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::BPOE< Real >::BPOE	(	const Real	threshold,
		const Real	order = `1`
	)

inline

Definition at line 91 of file ROL_BPOE.hpp.

References ROL::BPOE< Real >::hvec_.

template<class Real >

ROL::BPOE< Real >::BPOE ( ROL::ParameterList & parlist )

inline

Definition at line 96 of file ROL_BPOE.hpp.

References ROL::BPOE< Real >::hvec_, ROL::BPOE< Real >::order_, and ROL::BPOE< Real >::threshold_.

Member Function Documentation

template<class Real >

void ROL::BPOE< Real >::initialize ( const Vector< Real > & x )

inlinevirtual

Initialize temporary variables.

Parameters

[in] x is a vector used for initializing storage

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 103 of file ROL_BPOE.hpp.

References ROL::Vector< Real >::dual(), ROL::BPOE< Real >::dualVec1_, ROL::BPOE< Real >::dualVec2_, ROL::BPOE< Real >::firstResetBPOE_, ROL::BPOE< Real >::hvec_, and ROL::RandVarFunctional< Real >::initialize().

template<class Real >

void ROL::BPOE< Real >::updateValue	(	Objective< Real > &	obj,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol
	)

inlinevirtual

Update internal storage for value computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	weight	is the weight associated with the current sample point

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 115 of file ROL_BPOE.hpp.

References ROL::RandVarFunctional< Real >::computeValue(), ROL::BPOE< Real >::order_, ROL::BPOE< Real >::threshold_, ROL::RandVarFunctional< Real >::val_, ROL::RandVarFunctional< Real >::weight_, and zero.

template<class Real >

Real ROL::BPOE< Real >::getValue	(	const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		SampleGenerator< Real > &	sampler
	)

inlinevirtual

Return risk measure value.

Parameters

[in] sampler is the ROL::SampleGenerator used to sample the objective function

Upon return, getValue returns \(\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 127 of file ROL_BPOE.hpp.

References ROL::BPOE< Real >::order_, ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.

template<class Real >

void ROL::BPOE< Real >::updateGradient	(	Objective< Real > &	obj,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol
	)

inlinevirtual

Update internal risk measure storage for gradient computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	g	is the gradient of the random variable objective function at the current sample point
[in]	weight	is the weight associated with the current sample point

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 136 of file ROL_BPOE.hpp.

References ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::gv_, ROL::BPOE< Real >::order_, ROL::BPOE< Real >::threshold_, ROL::RandVarFunctional< Real >::val_, ROL::RandVarFunctional< Real >::weight_, and zero.

template<class Real >

void ROL::BPOE< Real >::getGradient	(	Vector< Real > &	g,
		std::vector< Real > &	gstat,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		SampleGenerator< Real > &	sampler
	)

inlinevirtual

Return risk measure (sub)gradient.

Parameters

[out]	g	is the (sub)gradient of the risk measure
[in]	sampler	is the ROL::SampleGenerator used to sample the objective function

Upon return, getGradient returns \(\theta\in\partial\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\) and \(\partial\mathcal{R}(X)\) denotes the subdifferential of \(\mathcal{R}\) at \(X\).

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 153 of file ROL_BPOE.hpp.

References ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::gv_, ROL::BPOE< Real >::order_, ROL::Vector< Real >::scale(), ROL::SampleGenerator< Real >::sumAll(), ROL::RandVarFunctional< Real >::val_, zero, and ROL::Vector< Real >::zero().

template<class Real >

void ROL::BPOE< Real >::updateHessVec	(	Objective< Real > &	obj,
		const Vector< Real > &	v,
		const std::vector< Real > &	vstat,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol
	)

inlinevirtual

Update internal risk measure storage for Hessian-time-a-vector computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	g	is the gradient of the random variable objective function at the current sample point
[in]	gv	is the gradient of the random variable objective function at the current sample point applied to the vector v0
[in]	hv	is the Hessian of the random variable objective function at the current sample point applied to the vector v0
[in]	weight	is the weight associated with the current sample point

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 174 of file ROL_BPOE.hpp.

References ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::BPOE< Real >::dualVec1_, ROL::BPOE< Real >::dualVec2_, ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::hv_, ROL::BPOE< Real >::hvec_, ROL::BPOE< Real >::order_, ROL::BPOE< Real >::threshold_, ROL::RandVarFunctional< Real >::weight_, and zero.

template<class Real >

void ROL::BPOE< Real >::getHessVec	(	Vector< Real > &	hv,
		std::vector< Real > &	hvstat,
		const Vector< Real > &	v,
		const std::vector< Real > &	vstat,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		SampleGenerator< Real > &	sampler
	)

inlinevirtual

Return risk measure Hessian-times-a-vector.

Parameters

[out]	hv	is the Hessian-times-a-vector of the risk measure
[in]	sampler	is the ROL::SampleGenerator used to sample the objective function

Upon return, getHessVec returns \(\nabla^2 \mathcal{R}(f(x_0))v_0\) (if available) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 206 of file ROL_BPOE.hpp.

References ROL::Vector< Real >::axpy(), ROL::BPOE< Real >::dualVec1_, ROL::BPOE< Real >::dualVec2_, ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::hv_, ROL::BPOE< Real >::hvec_, ROL::BPOE< Real >::order_, ROL::Vector< Real >::scale(), ROL::SampleGenerator< Real >::sumAll(), and zero.