/usr/include/trilinos/ROL_Chi2Divergence.hpp is in libtrilinos-rol-dev 12.12.1-5.
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// Rapid Optimization Library (ROL) Package
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#ifndef ROL_CHI2DIVERGENCE_HPP
#define ROL_CHI2DIVERGENCE_HPP
#include "ROL_FDivergence.hpp"
/** @ingroup risk_group
\class ROL::Chi2Divergence
\brief Provides an interface for the chi-squared-divergence distributionally robust
expectation.
This class defines a risk measure \f$\mathcal{R}\f$ that arises in distributionally
robust stochastic programming. \f$\mathcal{R}\f$ is given by
\f[
\mathcal{R}(X) = \sup_{\vartheta\in\mathfrak{A}}
\mathbb{E}[\vartheta X]
\f]
where \f$\mathfrak{A}\f$ is called the ambiguity (or uncertainty) set and
is defined by a constraint on the \f$\chi^2\f$-divergence, i.e.,
\f[
\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\}.
\f]
\f$\mathcal{R}\f$ is a law-invariant, coherent risk measure.
*/
namespace ROL {
template<class Real>
class Chi2Divergence : public FDivergence<Real> {
public:
/** \brief Constructor.
@param[in] thresh is the tolerance for the F-divergence constraint
*/
Chi2Divergence(const Real thresh) : FDivergence<Real>(thresh) {}
/** \brief Constructor.
@param[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
\li "Threshold" (greater than 0)
*/
Chi2Divergence(Teuchos::ParameterList &parlist) : FDivergence<Real>(parlist) {}
Real Fprimal(Real x, int deriv = 0) {
Real zero(0), one(1), half(0.5), val(0);
if (deriv==0) {
val = (x < zero) ? ROL_INF<Real>() : half*(x-one)*(x-one);
}
else if (deriv==1) {
val = (x < zero) ? ROL_INF<Real>() : x-one;
}
else if (deriv==2) {
val = (x < zero) ? ROL_INF<Real>() : one;
}
else {
TEUCHOS_TEST_FOR_EXCEPTION(true,std::invalid_argument,
">>> (ROL::Chi2Divergence): Derivative order must be 0, 1, or 2!");
}
return val;
}
Real Fdual(Real x, int deriv = 0) {
Real zero(0), one(1), half(0.5), val(0);
if (deriv==0) {
val = (x < -one) ? -half : (half*x + one)*x;
}
else if (deriv==1) {
val = (x < -one) ? zero : x + one;
}
else if (deriv==2) {
val = (x < -one) ? zero : one;
}
else {
TEUCHOS_TEST_FOR_EXCEPTION(true,std::invalid_argument,
">>> (ROL::Chi2Divergence): Derivative order must be 0, 1, or 2!");
}
return val;
}
};
}
#endif
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