/usr/include/trilinos/ROL_NonlinearCG.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_NONLINEARCG_H
#define ROL_NONLINEARCG_H
/** \class ROL::NonlinearCG
\brief Implements nonlinear conjugate gradient methods.
\detail Nonlinear CG methods have the update formulas
\f[ x_{k+1} = x_k + \alpha_k d_k \f]
\f[ d_{k+1} = -g_{k+1} + \beta_k d_k \f]
where \f$\alpha_k\f$ is a step length determined by a linesearch method
and \f$\beta_k\f$ is the parameter which distinguishes various CG methods.
The standard notation is that \f$ y_k = g_{k+1}-g_k \$f,
\f$ s_k = \alpha_k d_k = x_{k+1}-x_k \f$
Method | \f$\beta_k\f$
---------------------------|------------------------------------------------------
Hestenes-Stiefel | \f$ \frac{g_{k+1}^\top y_k}{d_k^\top y_k } \f$
Fletcher-Reeves | \f$ \frac{\|g_{k+1}\|^2}{\|g_k\|^2} \f$
Daniel (uses Hessian) | \f$ \frac{g_{k+1}^\top \nabla^2 f(x_k) d_k}{d_k^\top \nabla^2 f(x_k) d_k} \f$
Polak-Ribiere | \f$ \frac{g_{k+1}^\top y_k}{\|g_k\|^2} \f$
Fletcher Conjugate Descent | \f$ -\frac{\|g_{k+1}\|^2}{d_k^\top g_k} \f$
Liu-Storey | \f$ -\frac{g_k^\top y_{k-1} }{d_{k-1}^\top g_{k-1} \f$
Dai-Yuan | \f$ \frac{\|g_{k+1}\|^2}{d_k^\top y_k} \f$
Hager-Zhang | \f$ \frac{g_{k+1}^\top y_k}{d_k^\top y_k} - 2 \frac{\|y_k\|^2}{d_k^\top y_k} \frac{g_{k+1}^\top d_k}{d_k^\top y_k} \f$
Oren-Luenberger | \f$ \frac{g_{k+1}^\top y_k}{d_k^\top y_k} - \frac{\|y_k\|^2}{d_k^\top y_k} \frac{g_{k+1}^\top d_k}{d_k^\top y_k} \f$
*/
#include "ROL_Types.hpp"
namespace ROL {
template<class Real>
struct NonlinearCGState {
std::vector<Teuchos::RCP<Vector<Real> > > grad; // Gradient Storage
std::vector<Teuchos::RCP<Vector<Real> > > pstep; // Step Storage
int iter; // Nonlinear-CG Iteration Counter
int restart; // Reinitialize every 'restart' iterations
ENonlinearCG nlcg_type; // Nonlinear-CG Type
};
template<class Real>
class NonlinearCG {
private:
Teuchos::RCP<NonlinearCGState<Real> > state_; // Nonlinear-CG State
Teuchos::RCP<Vector<Real> > y_;
Teuchos::RCP<Vector<Real> > yd_;
public:
virtual ~NonlinearCG() {}
// Constructor
NonlinearCG(ENonlinearCG type, int restart = 100) {
state_ = Teuchos::rcp( new NonlinearCGState<Real> );
state_->iter = 0;
state_->grad.resize(1);
state_->pstep.resize(1);
TEUCHOS_TEST_FOR_EXCEPTION(!(isValidNonlinearCG(type)),
std::invalid_argument,
">>> ERROR (ROL_NonlinearCG.hpp): Invalid nonlinear CG type in constructor!");
state_->nlcg_type = type;
TEUCHOS_TEST_FOR_EXCEPTION((restart < 1),
std::invalid_argument,
">>> ERROR (ROL_NonlinearCG.hpp): Non-positive restart integer in constructor!");
state_->restart = restart;
}
Teuchos::RCP<NonlinearCGState<Real> >& get_state() { return this->state_; }
// Run one step of nonlinear CG.
virtual void run( Vector<Real> &s , const Vector<Real> &g, const Vector<Real> &x, Objective<Real> &obj ) {
Real one(1);
// Initialize vector storage
if ( state_->iter == 0 ) {
if ( state_->nlcg_type != NONLINEARCG_FLETCHER_REEVES &&
state_->nlcg_type != NONLINEARCG_FLETCHER_CONJDESC ) {
y_ = g.clone();
}
if ( state_->nlcg_type == NONLINEARCG_HAGER_ZHANG ||
state_->nlcg_type == NONLINEARCG_OREN_LUENBERGER ) {
yd_ = g.clone();
}
}
s.set(g.dual());
if ((state_->iter % state_->restart) != 0) {
Real beta(0), zero(0);
switch(state_->nlcg_type) {
case NONLINEARCG_HESTENES_STIEFEL: {
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
beta = - g.dot(*y_) / (state_->pstep[0]->dot(y_->dual()));
beta = std::max(beta, zero);
break;
}
case NONLINEARCG_FLETCHER_REEVES: {
beta = g.dot(g) / (state_->grad[0])->dot(*(state_->grad[0]));
break;
}
case NONLINEARCG_DANIEL: {
Real htol(0);
obj.hessVec( *y_, *(state_->pstep[0]), x, htol );
beta = - g.dot(*y_) / (state_->pstep[0])->dot(y_->dual());
beta = std::max(beta, zero);
break;
}
case NONLINEARCG_POLAK_RIBIERE: {
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
beta = g.dot(*y_) / (state_->grad[0])->dot(*(state_->grad[0]));
beta = std::max(beta, zero);
break;
}
case NONLINEARCG_FLETCHER_CONJDESC: {
beta = g.dot(g) / (state_->pstep[0])->dot((state_->grad[0])->dual());
break;
}
case NONLINEARCG_LIU_STOREY: {
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
beta = g.dot(*y_) / (state_->pstep[0])->dot((state_->grad[0])->dual());
//beta = std::max(beta, 0.0); // Is this needed? May need research.
break;
}
case NONLINEARCG_DAI_YUAN: {
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
beta = - g.dot(g) / (state_->pstep[0])->dot(y_->dual());
break;
}
case NONLINEARCG_HAGER_ZHANG: {
Real eta_0(1e-2), two(2);
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
yd_->set(*y_);
Real mult = two * ( y_->dot(*y_) / (state_->pstep[0])->dot(y_->dual()) );
yd_->axpy(-mult, (state_->pstep[0])->dual());
beta = - yd_->dot(g) / (state_->pstep[0])->dot(y_->dual());
Real eta = -one / ((state_->pstep[0])->norm()*std::min(eta_0,(state_->grad[0])->norm()));
beta = std::max(beta, eta);
break;
}
case NONLINEARCG_OREN_LUENBERGER: {
Real eta_0(1e-2);
y_->set(g);
y_->axpy(-one, *(state_->grad[0]));
yd_->set(*y_);
Real mult = ( y_->dot(*y_) / (state_->pstep[0])->dot(y_->dual()) );
yd_->axpy(-mult, (state_->pstep[0])->dual());
beta = - yd_->dot(g) / (state_->pstep[0])->dot(y_->dual());
Real eta = -one / ((state_->pstep[0])->norm()*std::min(eta_0,(state_->grad[0])->norm()));
beta = std::max(beta, eta);
break;
}
default:
TEUCHOS_TEST_FOR_EXCEPTION(!(isValidNonlinearCG(state_->nlcg_type)),
std::invalid_argument,
">>> ERROR (ROL_NonlinearCG.hpp): Invalid nonlinear CG type in the 'run' method!");
}
s.axpy(beta, *(state_->pstep[0]));
}
// Update storage.
if (state_->iter == 0) {
(state_->grad[0]) = g.clone();
(state_->pstep[0]) = s.clone();
}
(state_->grad[0])->set(g);
(state_->pstep[0])->set(s);
state_->iter++;
}
};
}
#endif
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