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// Rapid Optimization Library (ROL) Package
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#ifndef ROL_BISECTIONSCALARMINIMIZATION_H
#define ROL_BISECTIONSCALARMINIMIZATION_H
/** \class ROL::BisectionScalarMinimization
\brief Implements the bisection method to minimize a scalar function on a
bounded interval.
*/
#include "ROL_ScalarMinimization.hpp"
#include "ROL_ScalarFunction.hpp"
#include "ROL_Types.hpp"
namespace ROL {
template<class Real>
class BisectionScalarMinimization : public ScalarMinimization<Real> {
private:
Real tol_;
int niter_;
public:
// Constructor
BisectionScalarMinimization( Teuchos::ParameterList &parlist ) {
Teuchos::ParameterList &list = parlist.sublist("Scalar Minimization").sublist("Bisection");
tol_ = list.get("Tolerance",1.e-10);
niter_ = list.get("Iteration Limit",1000);
}
void run(Real &fx, Real &x, int &nfval, int &ngrad,
ScalarFunction<Real> &f, const Real A, const Real B,
ScalarMinimizationStatusTest<Real> &test) const {
Real zero(0), half(0.5);
nfval = 0; ngrad = 0;
// Compute value f(A) and f(B)
Real a = A, fa = f.value(a); nfval++;
Real b = B, fb = f.value(b); nfval++;
Real m = half*(A+B), fm = f.value(m); nfval++;
Real u = zero, fu = zero, v = zero, fv = zero, gx = ROL_INF<Real>();
bool deriv = false;
// Get minimum of all evaluations
if ( fa <= fm && fa <= fb ) {
x = a; fx = fa;
}
else if ( fm <= fa && fm <= fb ) {
x = m; fx = fm;
}
else {
x = b; fx = fb;
}
// Run bisection
for ( int i = 0; i < niter_; i++ ) {
if ( std::abs(b - a) < tol_ || test.check(x,fx,gx,nfval,ngrad,deriv) ) {
break;
}
u = half*(a+m); fu = f.value(u); nfval++;
v = half*(m+b); fv = f.value(v); nfval++;
if ( ( (fa <= fb) && (fa <= fu) && (fa <= fv) && (fa <= fm) )
|| ( (fu <= fb) && (fu <= fa) && (fu <= fv) && (fu <= fm) ) ) {
if ( fa < fu ) {
x = a; fx = fa;
}
else {
x = u; fx = fu;
}
b = m; fb = fm;
m = u; fm = fu;
}
else if ( ( (fm <= fb) && (fm <= fa) && (fm <= fu) && (fm <= fv) ) ) {
x = m; fx = fm;
a = u; fa = fu;
b = v; fb = fv;
}
else if ( ( (fv <= fb) && (fv <= fa) && (fv <= fu) && (fv <= fm) )
|| ( (fb <= fa) && (fb <= fu) && (fb <= fv) && (fb <= fm) ) ) {
if ( fb < fv ) {
x = b; fx = fb;
}
else {
x = v; fx = fv;
}
a = m; fa = fm;
m = v; fm = fv;
}
}
}
};
}
#endif
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