ROL::Chi2Divergence< Real > Class Template Reference

Provides an interface for the chi-squared-divergence distributionally robust expectation. More...

#include <ROL_Chi2Divergence.hpp>

Inheritance diagram for ROL::Chi2Divergence< Real >:

Public Member Functions
	Chi2Divergence (const Real thresh)
	Constructor.
	Chi2Divergence (ROL::ParameterList &parlist)
	Constructor.
Real	Fprimal (Real x, int deriv=0) const
	Implementation of the scalar primal F function.
Real	Fdual (Real x, int deriv=0) const
	Implementation of the scalar dual F function.
Public Member Functions inherited from ROL::FDivergence< Real >
	FDivergence (const Real thresh)
	Constructor.
	FDivergence (ROL::ParameterList &parlist)
	Constructor.
bool	check (std::ostream &outStream=std::cout) const
void	initialize (const Vector< Real > &x)
void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
void	updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
void	getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
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)
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)

Detailed Description

template<class Real>
class ROL::Chi2Divergence< Real >

Provides an interface for the chi-squared-divergence distributionally robust expectation.

This class defines a risk measure \(\mathcal{R}\) that arises in distributionally robust stochastic programming. \(\mathcal{R}\) is given by

\[ \mathcal{R}(X) = \sup_{\vartheta\in\mathfrak{A}} \mathbb{E}[\vartheta X] \]

where \(\mathfrak{A}\) is called the ambiguity (or uncertainty) set and is defined by a constraint on the \(\chi^2\)-divergence, i.e.,

\[ \mathfrak{A} = \left\{\vartheta\in\mathcal{X}^*\,:\, \mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\; \frac{1}{2}\mathbb{E}[(\vartheta-1)^2] \le \epsilon\right\}. \]

\(\mathcal{R}\) is a law-invariant, coherent risk measure.

Definition at line 39 of file ROL_Chi2Divergence.hpp.

Constructor & Destructor Documentation

Chi2Divergence() [1/2]

template<class Real>

ROL::Chi2Divergence< Real >::Chi2Divergence ( const Real thresh )

inline

Constructor.

Parameters

[in]

thresh

is the tolerance for the F-divergence constraint

Definition at line 46 of file ROL_Chi2Divergence.hpp.

References ROL::FDivergence< Real >::FDivergence().

Chi2Divergence() [2/2]

template<class Real>

ROL::Chi2Divergence< Real >::Chi2Divergence ( ROL::ParameterList & parlist )

inline

Constructor.

Parameters

[in]

parlist

is a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measure"->"F-Divergence" and within the "F-Divergence" sublist should have the following parameters

• "Threshold" (greater than 0)

Definition at line 56 of file ROL_Chi2Divergence.hpp.

References ROL::FDivergence< Real >::FDivergence().

Member Function Documentation

Fprimal()

template<class Real>

Real ROL::Chi2Divergence< Real >::Fprimal ( Real x, int deriv = 0 ) const

inlinevirtual

Implementation of the scalar primal F function.

Parameters

[in]	x	is a scalar input
[in]	deriv	is the derivative order

Upon return, Fprimal returns \(F(x)\) or a derivative of \(F(x)\).

Implements ROL::FDivergence< Real >.

Definition at line 58 of file ROL_Chi2Divergence.hpp.

References zero.

Fdual()

template<class Real>

Real ROL::Chi2Divergence< Real >::Fdual ( Real x, int deriv = 0 ) const

inlinevirtual

Implementation of the scalar dual F function.

Parameters

[in]	x	is a scalar input
[in]	deriv	is the derivative order

Upon return, Fdual returns \(F^*(x)\) or a derivative of \(F^*(x)\). Here, \(F^*\) denotes the Legendre-Fenchel transformation of \(F\), i.e.,

\[ F^*(y) = \sup_{x\in\mathbb{R}}\{xy - F(x)\}. \]

Implements ROL::FDivergence< Real >.

Definition at line 76 of file ROL_Chi2Divergence.hpp.

References zero.

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

• ROL_Chi2Divergence.hpp