ROL_BVP.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_BVP_HPP
#define ROL_BVP_HPP

#include "ROL_ScaledStdVector.hpp"
#include "ROL_TestProblem.hpp"
#include "ROL_Bounds.hpp"

namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_BVP : public Objective<Real> {

  typedef typename std::vector<Real>::size_type uint;

  private: 
    uint dim_;

  public:
    Objective_BVP(void) : dim_(20) {}

    Real value( const Vector<Real> &x, Real &tol ) {
      Ptr<const std::vector<Real> > ex
        = dynamic_cast<const StdVector<Real>&>(x).getVector(); 

      Real val = 0.0;
      Real f   = 0.0;
      Real h   = 1.0/((Real)(dim_) + 1.0);
      for ( uint i = 0; i < dim_; i++ ) {
        f = 2.0*(*ex)[i] + h*h*std::pow((*ex)[i] + (Real)(i+1)*h + 1.0,3.0)/2.0; 
        if ( i < (dim_-1) ) { f -= (*ex)[i+1]; } 
        if ( i > 0 )              { f -= (*ex)[i-1]; }
        val += f*f;
      }
      return val; 
    }

    void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
      Ptr<std::vector<Real> > eg
        = dynamic_cast<StdVector<Real>&>(g).getVector(); 
      Ptr<const std::vector<Real> > ex
        = dynamic_cast<const StdVector<Real>&>(x).getVector(); 

      g.zero();
      Real h  = 1.0/((Real)(dim_) + 1.0);
      std::vector<Real> f(dim_,0.0);

      for ( uint i = 0; i < dim_; i++ ) {
        f[i] = 2.0*(*ex)[i] + h*h*std::pow((*ex)[i] + (Real)(i+1)*h + 1.0,3.0)/2.0;
        if ( i < (dim_-1) ) { f[i] -= (*ex)[i+1]; }
        if ( i > 0)               { f[i] -= (*ex)[i-1]; }
      }
      Real df = 0.0;
      for ( uint i = 0; i < dim_; i++ ) {
        df = (2.0 + 3.0*h*h*std::pow((*ex)[i] + (Real)(i+1)*h + 1.0,2.0)/2.0)*f[i];
        if ( i < (dim_-1) ) { df -= f[i+1]; }
        if ( i > 0 )        { df -= f[i-1]; }
        (*eg)[i] += 2.0*df;
      }
    }
#if USE_HESSVEC
    void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
      Ptr<std::vector<Real> > ehv
        = dynamic_cast<StdVector<Real>&>(hv).getVector(); 
      Ptr<const std::vector<Real> > ev
        = dynamic_cast<const StdVector<Real>&>(v).getVector(); 
      Ptr<const std::vector<Real> > ex
        = dynamic_cast<const StdVector<Real>&>(x).getVector(); 

      hv.zero();
      Real h = 1.0/((Real)(dim_) + 1.0);
      Real f = 0.0, df = 0.0, dfn = 0.0, hf = 0.0;
      for ( uint i = 0; i < dim_; i++ ) {
        f  = 2.0*(*ex)[i] + h*h*std::pow((*ex)[i] + (Real)(i+1)*h + 1.0,3.0)/2.0;
        df = 2.0 + 3.0/2.0 * h*h * std::pow((*ex)[i] + (Real)(i+1)*h + 1.0,2.0);
        hf = 3.0 * h*h * ((*ex)[i] + (Real)(i+1)*h + 1.0);
        if ( i < (dim_-2) ) {
          (*ehv)[i] += 2.0*(*ev)[i+2];
        }
        if ( i < (dim_-1) ) {
          f -= (*ex)[i+1];
          dfn = 2.0 + 3.0/2.0 * h*h * std::pow((*ex)[i+1] + (Real)(i+2)*h + 1.0,2.0);
          (*ehv)[i] -= 2.0*(df + dfn)*(*ev)[i+1];
          (*ehv)[i] += 2.0*(*ev)[i];
        }
        if ( i > 0 ) {
          f -= (*ex)[i-1];
          dfn = 2.0 + 3.0/2.0 * h*h * std::pow((*ex)[i-1] + (Real)(i)*h + 1.0,2.0);
          (*ehv)[i] -= 2.0*(df + dfn)*(*ev)[i-1];
          (*ehv)[i] += 2.0*(*ev)[i];
        }  
        if ( i > 1 ) {
          (*ehv)[i] += 2.0*(*ev)[i-2];
        } 
        (*ehv)[i] += 2.0*(hf*f + df*df)*(*ev)[i];  
      }
    } 
#endif
  };

  template<class Real>
  class getBVP : public TestProblem<Real> {
  private:
    int n_;
    Ptr<std::vector<Real> > scale_;

  public:
    getBVP(void) {
      n_ = 20;
      scale_ = makePtr<std::vector<Real>>(n_,0.0);
      (*scale_)[0]  = 1.e2;
      (*scale_)[1]  = 1.e2;
      (*scale_)[2]  = 1.e2;
      (*scale_)[3]  = 1.e2;
      (*scale_)[4]  = 1.e2;
      (*scale_)[5]  = 1.e2;
      (*scale_)[6]  = 1.e2;
      (*scale_)[7]  = 1.e2;
      (*scale_)[8]  = 1.e2;
      (*scale_)[9]  = 1.e2;
      (*scale_)[10] = 1.e2;
      (*scale_)[11] = 1.e2;
      (*scale_)[12] = 1.e2;
      (*scale_)[13] = 1.e2;
      (*scale_)[14] = 1.e2;
      (*scale_)[15] = 1.e2;
      (*scale_)[16] = 1.e4;
      (*scale_)[17] = 1.e4;
      (*scale_)[18] = 1.e4;
      (*scale_)[19] = 1.e6;
    }

    Ptr<Objective<Real>> getObjective(void) const {
      return makePtr<Objective_BVP<Real>>();
    }

    Ptr<Vector<Real>> getInitialGuess(void) const {
      // Get Initial Guess
      Ptr<std::vector<Real> > x0p = makePtr<std::vector<Real>>(n_,0.0);
      Real h = 1.0/((Real)n_ + 1.0);
      for ( int i = 0; i < n_; i++ ) {
        (*x0p)[i] = (Real)(i+1)*h*((Real)(i+1)*h - 1.0);
      }
      return makePtr<PrimalScaledStdVector<Real>>(x0p,scale_);
    }

    Ptr<Vector<Real>> getSolution(const int i = 0) const {
      // Get Solution
      Ptr<std::vector<Real> > xp  = makePtr<std::vector<Real>>(n_,0.0);
      (*xp)[0]  = 1.2321000000000001e-01; 
      (*xp)[1]  = 2.1743122909175336e-01;
      (*xp)[2]  = 2.8625218549543746e-01;
      (*xp)[3]  = 3.3309751851140840e-01;
      (*xp)[4]  = 3.6117201714254760e-01;
      (*xp)[5]  = 3.7342787212179440e-01;
      (*xp)[6]  = 3.7255212003706123e-01;
      (*xp)[7]  = 3.6096984201471016e-01;
      (*xp)[8]  = 3.4085861052124522e-01;
      (*xp)[9]  = 3.1417024791439530e-01;
      (*xp)[10] = 2.8265678244892922e-01; 
      (*xp)[11] = 2.4789833165179542e-01;
      (*xp)[12] = 2.1133139591375166e-01;
      (*xp)[13] = 1.7427666644258599e-01;
      (*xp)[14] = 1.3796594229036069e-01;
      (*xp)[15] = 1.0356813245768780e-01;
      (*xp)[16] = 7.2214621084083663e-02;
      (*xp)[17] = 4.5024529114833199e-02;
      (*xp)[18] = 2.3130648161534966e-02;
      (*xp)[19] = 7.7070870882527927e-03;
      return makePtr<PrimalScaledStdVector<Real>>(xp,scale_);
    }

    Ptr<BoundConstraint<Real>> getBoundConstraint(void) const {
      // Instantiate BoundConstraint
      Ptr<std::vector<Real> > lp = makePtr<std::vector<Real>>();
      Ptr<std::vector<Real> > up = makePtr<std::vector<Real>>();
      std::vector<Real> val(n_,0.0); 
      val[0] = 0.1*0.2321;
      val[1] = -0.1*0.4520;
      val[2] = -0.1*0.6588;
      val[3] = -0.1*0.8514;
      val[4] = -0.1*1.0288;
      val[5] = -0.1*1.1985;
      val[6] = -0.1*1.3322;
      val[7] = -0.1*1.4553;
      val[8] = -0.1*1.5571;
      val[9] = -0.1*1.6354;
      val[10] = -0.1*1.6881;
      val[11] = -0.1*1.7127;
      val[12] = -0.1*1.7060;
      val[13] = -0.1*1.6650;
      val[14] = -0.1*1.5856;
      val[15] = -0.1*1.4636;
      val[16] = -0.1*1.2938;
      val[17] = -0.1*1.0702;
      val[18] = -0.1*0.7858;
      val[19] = -0.1*0.4323;
      for ( int i = 0; i < n_; i++ ) { 
        if ( i%2 == 0 ) {  
          lp->push_back(std::max(-0.2*(Real)(n_),val[i]+0.1));
          up->push_back(std::min( 0.2*(Real)(n_),val[i]+1.1));
        }
        else {
          lp->push_back(-0.2*(Real)(n_));
          up->push_back( 0.2*(Real)(n_));
        }
      }
      Ptr<Vector<Real> > l = makePtr<StdVector<Real>>(lp);
      Ptr<Vector<Real> > u = makePtr<StdVector<Real>>(up);
      return makePtr<Bounds<Real>>(l,u);
    }
  };

}// End ZOO Namespace
}// End ROL Namespace

#endif