ROL_DoubleDogLeg.hpp

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// @HEADER
// *****************************************************************************
//               Rapid Optimization Library (ROL) Package
//
// Copyright 2014 NTESS and the ROL contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef ROL_DOUBLEDOGLEG_H
#define ROL_DOUBLEDOGLEG_H

#include "ROL_TrustRegion.hpp"
#include "ROL_Types.hpp"

namespace ROL { 

template<class Real>
class DoubleDogLeg : public TrustRegion<Real> {
private:

  ROL::Ptr<CauchyPoint<Real> > cpt_;

  ROL::Ptr<Vector<Real> > s_;
  ROL::Ptr<Vector<Real> > v_;
  ROL::Ptr<Vector<Real> > Hp_;

  Real pRed_;

public:

  // Constructor
  DoubleDogLeg( ROL::ParameterList &parlist ) : TrustRegion<Real>(parlist), pRed_(0) {
    cpt_ = ROL::makePtr<CauchyPoint<Real>>(parlist);
  }

  void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g) {
    TrustRegion<Real>::initialize(x,s,g);
    cpt_->initialize(x,s,g);
    s_ = s.clone();
    v_ = s.clone();
    Hp_ = g.clone();
  }

  void run( Vector<Real>           &s,
            Real                   &snorm,
            int                    &iflag,
            int                    &iter,
            const Real              del,
            TrustRegionModel<Real> &model ) {
    Real tol = std::sqrt(ROL_EPSILON<Real>());
    const Real one(1), zero(0), half(0.5), p2(0.2), p8(0.8), two(2);
    // Set s to be the (projected) gradient
    model.dualTransform(*Hp_,*model.getGradient());
    s.set(Hp_->dual());
    // Compute (quasi-)Newton step
    model.invHessVec(*s_,*Hp_,s,tol);
    Real sNnorm  = s_->norm();
    Real tmp     = -s_->dot(s);
    bool negCurv = (tmp > zero ? true : false);
    Real gsN = std::abs(tmp);
    // Check if (quasi-)Newton step is feasible
    if ( negCurv ) {
      // Use Cauchy point
      cpt_->run(s,snorm,iflag,iter,del,model);
      pRed_ = cpt_->getPredictedReduction();
      iflag = 2;
    }
    else {
      // Approximately solve trust region subproblem using double dogleg curve
      if (sNnorm <= del) { // Use the (quasi-)Newton step
        s.set(*s_); 
        s.scale(-one);
        snorm = sNnorm;
        pRed_ = half*gsN;
        iflag = 0;
      }
      else { // The (quasi-)Newton step is outside of trust region
        model.hessVec(*Hp_,s,s,tol);
        Real alpha  = zero;
        Real beta   = zero;
        Real gnorm  = s.norm();
        Real gnorm2 = gnorm*gnorm;
        Real gBg    = Hp_->dot(s.dual());
        Real gamma1 = gnorm/gBg;
        Real gamma2 = gnorm/gsN;
        Real eta    = p8*gamma1*gamma2 + p2;
        if (eta*sNnorm <= del || gBg <= zero) { // Dogleg Point is inside trust region
          alpha = del/sNnorm;
          beta  = zero;
          s.set(*s_);
          s.scale(-alpha);
          snorm = del;
          iflag = 1;
        }
        else {
          if (gnorm2*gamma1 >= del) { // Cauchy Point is outside trust region
            alpha = zero;
            beta  = -del/gnorm;
            s.scale(beta); 
            snorm = del;
            iflag = 2;
          }
          else {              // Find convex combination of Cauchy and Dogleg point
            s.scale(-gamma1*gnorm);
            v_->set(s);
            v_->axpy(eta,*s_);
            v_->scale(-one);
            Real wNorm = v_->dot(*v_);
            Real sigma = del*del-std::pow(gamma1*gnorm,two);
            Real phi   = s.dot(*v_);
            Real theta = (-phi + std::sqrt(phi*phi+wNorm*sigma))/wNorm;
            s.axpy(theta,*v_); 
            snorm = del;
            alpha = theta*eta;
            beta  = (one-theta)*(-gamma1*gnorm);
            iflag = 3;
          }
        }
        pRed_ = -(alpha*(half*alpha-one)*gsN + half*beta*beta*gBg + beta*(one-alpha)*gnorm2);
      }
    }
    model.primalTransform(*s_,s);
    s.set(*s_);
    snorm = s.norm();
    TrustRegion<Real>::setPredictedReduction(pRed_);
  }
};

}

#endif