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// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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#ifndef ROL_CUBICINTERP_H
#define ROL_CUBICINTERP_H
/** \class ROL::CubicInterp
\brief Implements cubic interpolation back tracking line search.
*/
#include "ROL_LineSearch.hpp"
namespace ROL {
template<class Real>
class CubicInterp : public LineSearch<Real> {
private:
Real rho_;
Teuchos::RCP<Vector<Real> > xnew_;
public:
virtual ~CubicInterp() {}
// Constructor
CubicInterp( Teuchos::ParameterList &parlist ) : LineSearch<Real>(parlist) {
Real half(0.5);
rho_ = parlist.sublist("Step").sublist("Line Search").sublist("Line-Search Method").get("Backtracking Rate",half);
}
void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g,
Objective<Real> &obj, BoundConstraint<Real> &con ) {
LineSearch<Real>::initialize(x,s,g,obj,con);
xnew_ = x.clone();
}
void run( Real &alpha, Real &fval, int &ls_neval, int &ls_ngrad,
const Real &gs, const Vector<Real> &s, const Vector<Real> &x,
Objective<Real> &obj, BoundConstraint<Real> &con ) {
Real tol = std::sqrt(ROL_EPSILON<Real>());
ls_neval = 0;
ls_ngrad = 0;
// Get initial line search parameter
alpha = LineSearch<Real>::getInitialAlpha(ls_neval,ls_ngrad,fval,gs,x,s,obj,con);
// Update iterate
LineSearch<Real>::updateIterate(*xnew_,x,s,alpha,con);
// Get objective value at xnew
Real fold = fval;
obj.update(*xnew_);
fval = obj.value(*xnew_,tol);
ls_neval++;
// Initialize
Real fvalp(0), alpha1(0), alpha2(0), a(0), b(0), x1(0), x2(0);
const Real one(1), two(2), three(3), half(0.5), p1(0.1);
bool first_iter = true;
// Perform cubic interpolation back tracking
while ( !LineSearch<Real>::status(LINESEARCH_CUBICINTERP,ls_neval,ls_ngrad,alpha,fold,gs,fval,x,s,obj,con) ) {
if ( first_iter ) { // Minimize quadratic interpolate
alpha1 = -gs*alpha*alpha/(two*(fval-fold-gs*alpha));
first_iter = false;
}
else { // Minimize cubic interpolate
x1 = fval-fold-alpha*gs;
x2 = fvalp-fval-alpha2*gs;
a = (one/(alpha - alpha2))*( x1/(alpha*alpha) - x2/(alpha2*alpha2));
b = (one/(alpha - alpha2))*(-x1*alpha2/(alpha*alpha) + x2*alpha/(alpha2*alpha2));
if ( std::abs(a) < ROL_EPSILON<Real>() ) {
alpha1 = -gs/(two*b);
}
else {
alpha1 = (-b+sqrt(b*b-three*a*gs))/(three*a);
}
if ( alpha1 > half*alpha ) {
alpha1 = half*alpha;
}
}
alpha2 = alpha;
fvalp = fval;
// Back track if necessary
if ( alpha1 <= p1*alpha ) {
alpha *= p1;
}
else if ( alpha1 >= half*alpha ) {
alpha *= half;
}
else {
alpha = alpha1;
}
// Update iterate
LineSearch<Real>::updateIterate(*xnew_,x,s,alpha,con);
// Get objective value at xnew
obj.update(*xnew_);
fval = obj.value(*xnew_,tol);
ls_neval++;
}
}
};
}
#endif
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