ROL_Quartic.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_QUARTIC_HPP
#define ROL_QUARTIC_HPP

#include "ROL_ScaledStdVector.hpp"
#include "ROL_StdObjective.hpp"
#include "ROL_StdConstraint.hpp"
#include "ROL_TestProblem.hpp"

namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_Quartic : public StdObjective<Real> {
  public:
    Objective_Quartic() {}

    Real value( const std::vector<Real> &x, Real &tol ) {
      const Real one(1);
      return std::pow(x[0]-one, 4) + std::pow(x[1]-one, 4);
    }

    void gradient( std::vector<Real> &g, const std::vector<Real> &x, Real &tol ) {
      const Real one(1), four(4);
      g[0] = four * std::pow(x[0]-one, 3);
      g[1] = four * std::pow(x[1]-one, 3);
    }
#if USE_HESSVEC
    void hessVec( std::vector<Real> &hv, const std::vector<Real> &v, const std::vector<Real> &x, Real &tol ) {
      const Real one(1), twelve(12);
      hv[0] = twelve * std::pow(x[0]-one, 2) * v[0];
      hv[1] = twelve * std::pow(x[1]-one, 2) * v[1];
    }
#endif
  };

  template<class Real>
  class Constraint_Quartic : public StdConstraint<Real> {
  public:
    Constraint_Quartic() {}

    void value( std::vector<Real> &c, const std::vector<Real> &x, Real &tol ) {
      const Real half(0.5);
      c[0] = std::pow(x[0], 2) - half*x[1];
      c[1] = std::pow(x[1], 2) - half*x[0];
    }

    void applyJacobian( std::vector<Real> &jv, const std::vector<Real> &v, const std::vector<Real> &x, Real &tol ) {
      const Real half(0.5), two(2);
      jv[0] = two*x[0]*v[0] - half*v[1];
      jv[1] = two*x[1]*v[1] - half*v[0];
    }

    void applyAdjointJacobian( std::vector<Real> &ajv, const std::vector<Real> &v, const std::vector<Real> &x, Real &tol ) {
      const Real half(0.5), two(2);
      ajv[0] = two*x[0]*v[0] - half*v[1];
      ajv[1] = two*x[1]*v[1] - half*v[0];
    }
#if USE_HESSVEC
    void applyAdjointHessian( std::vector<Real> &ahuv, const std::vector<Real> &u, const std::vector<Real> &v, const std::vector<Real> &x, Real &tol ) {
      const Real two(2);
      ahuv[0] = two*u[0]*v[0];
      ahuv[1] = two*u[1]*v[1];
    }
#endif
  };

  template<class Real>
  class getQuartic : public TestProblem<Real> {
  public:
    getQuartic() {}

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

    Ptr<Vector<Real>> getInitialGuess(void) const {
      int n = 2;
      Ptr<std::vector<Real>> scale = makePtr<std::vector<Real>>(n,static_cast<Real>(1.0));
      Ptr<std::vector<Real>> xp    = makePtr<std::vector<Real>>(n,static_cast<Real>(1.0)); 
      return makePtr<PrimalScaledStdVector<Real>>(xp,scale);
    }

    Ptr<Vector<Real>> getSolution(const int i = 0) const {
      int n = 2;
      Ptr<std::vector<Real>> scale = makePtr<std::vector<Real>>(n,static_cast<Real>(1.0));
      Ptr<std::vector<Real>> xp    = makePtr<std::vector<Real>>(n,static_cast<Real>(0.5));
      return makePtr<PrimalScaledStdVector<Real>>(xp,scale);
    }

    Ptr<BoundConstraint<Real>> getBoundConstraint(void) const {
      int n = 2;
      Ptr<std::vector<Real>> scale = makePtr<std::vector<Real>>(n,static_cast<Real>(1.0));
      Ptr<std::vector<Real>> lp    = makePtr<std::vector<Real>>(n,static_cast<Real>(0.0));
      Ptr<std::vector<Real>> up    = makePtr<std::vector<Real>>(n,static_cast<Real>(0.0));
      (*lp)[0] = static_cast<Real>( 0.5);
      (*lp)[1] = static_cast<Real>(-2.9);
      (*up)[0] = static_cast<Real>( 5.8);
      (*up)[1] = static_cast<Real>( 2.9);
      Ptr<Vector<Real>> l = makePtr<PrimalScaledStdVector<Real>>(lp,scale);
      Ptr<Vector<Real>> u = makePtr<PrimalScaledStdVector<Real>>(up,scale);
      return makePtr<Bounds<Real>>(l,u);
    }

    Ptr<Constraint<Real>> getInequalityConstraint(void) const {
      return makePtr<Constraint_Quartic<Real>>();
    }

    Ptr<Vector<Real>> getInequalityMultiplier(void) const {
      Ptr<std::vector<Real>> scale = makePtr<std::vector<Real>>(2,static_cast<Real>(1.0));
      Ptr<std::vector<Real>> lp    = makePtr<std::vector<Real>>(2,static_cast<Real>(0.0)); 
      return makePtr<DualScaledStdVector<Real>>(lp,scale);
    }

    Ptr<BoundConstraint<Real>> getSlackBoundConstraint(void) const {
      Ptr<std::vector<Real>> scale = makePtr<std::vector<Real>>(2,static_cast<Real>(1.0));
      Ptr<std::vector<Real>> up    = makePtr<std::vector<Real>>(2,static_cast<Real>(0.0)); 
      Ptr<Vector<Real>> u = makePtr<DualScaledStdVector<Real>>(up,scale);
      return makePtr<Bounds<Real>>(*u,false);
    }
  };

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

#endif