Provides an interface for the mean plus variance risk measure using the expectation risk quadrangle. More...

#include <ROL_MeanVarianceQuadrangle.hpp>

Inheritance diagram for ROL::MeanVarianceQuadrangle< Real >:

Public Member Functions
	MeanVarianceQuadrangle (const Real coeff=1)
	Constructor. More...

	MeanVarianceQuadrangle (ROL::ParameterList &parlist)
	Constructor. More...

Real	error (Real x, int deriv=0)
	Evaluate the scalar error function at x. More...

Real	regret (Real x, int deriv=0)
	Evaluate the scalar regret function at x. More...

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

	ExpectationQuad (void)

virtual void	check (void)
	Run default derivative tests for the scalar regret function. More...

Private Member Functions
void	parseParameterList (ROL::ParameterList &parlist)

void	checkInputs (void) const

Private Attributes
Real	coeff_

Detailed Description

template<class Real>
class ROL::MeanVarianceQuadrangle< Real >

Provides an interface for the mean plus variance risk measure using the expectation risk quadrangle.

The mean plus variances risk measure is

\[ \mathcal{R}(X) = \mathbb{E}[X] + c \mathbb{E}[|X-\mathbb{E}[X]|^2] \]

where \(c \ge 0\). \(\mathcal{R}\) is law-invariant, but not coherent since it violates positive homogeneity. The associated scalar regret function is

\[ v(x) = c x^2 + x \]

and the mean-plus-variance risk measure is computed as

\[ \mathcal{R}(X) = \inf_{t\in\mathbb{R}}\left\{ t + \mathbb{E}[v(X-t)] \right\}. \]

ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(t\), then minimizes jointly for \((x_0,t)\).

Definition at line 78 of file ROL_MeanVarianceQuadrangle.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::MeanVarianceQuadrangle< Real >::MeanVarianceQuadrangle ( const Real coeff = 1 )

inline

Constructor.

Parameters

[in] coeff is the weight for variance term

Definition at line 109 of file ROL_MeanVarianceQuadrangle.hpp.

References ROL::MeanVarianceQuadrangle< Real >::checkInputs().

template<class Real >

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measure"->"Mean-Variance Quadrangle" and within the "Mean-Variance Quadrangle" sublist should have the following parameters