ROL
ROL_HS2.hpp
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43 
49 #ifndef USE_HESSVEC
50 #define USE_HESSVEC 1
51 #endif
52 
53 #ifndef ROL_HS2_HPP
54 #define ROL_HS2_HPP
55 
56 #include "ROL_StdVector.hpp"
57 #include "ROL_Objective.hpp"
58 #include "ROL_BoundConstraint.hpp"
59 #include "ROL_Types.hpp"
60 
61 namespace ROL {
62 namespace ZOO {
63 
66  template<class Real>
67  class Objective_HS2 : public Objective<Real> {
68 
69  typedef std::vector<Real> vector;
70  typedef Vector<Real> V;
72 
73  private:
74 
75  Teuchos::RCP<const vector> getVector( const V& x ) {
76  using Teuchos::dyn_cast;
77  return dyn_cast<const SV>(x).getVector();
78  }
79 
80  Teuchos::RCP<vector> getVector( V& x ) {
81  using Teuchos::dyn_cast;
82  return dyn_cast<SV>(x).getVector();
83  }
84 
85  public:
86  Objective_HS2(void) {}
87 
88  Real value( const Vector<Real> &x, Real &tol ) {
89 
90  using Teuchos::RCP;
91  RCP<const vector> ex = getVector(x);
92  return static_cast<Real>(100) * std::pow((*ex)[1] - std::pow((*ex)[0],2),2)
93  + std::pow(static_cast<Real>(1)-(*ex)[0],2);
94  }
95 
96  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
97 
98  using Teuchos::RCP;
99  RCP<const vector> ex = getVector(x);
100  RCP<vector> eg = getVector(g);
101  (*eg)[0] = static_cast<Real>(-400) * ((*ex)[1] - std::pow((*ex)[0],2))
102  * (*ex)[0] - static_cast<Real>(2) * (static_cast<Real>(1)-(*ex)[0]);
103  (*eg)[1] = static_cast<Real>(200) * ((*ex)[1] - std::pow((*ex)[0],2));
104  }
105 #if USE_HESSVEC
106  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
107 
108  using Teuchos::RCP;
109  RCP<const vector> ex = getVector(x);
110  RCP<const vector> ev = getVector(v);
111  RCP<vector> ehv = getVector(hv);
112 
113  Real h11 = static_cast<Real>(-400) * (*ex)[1]
114  + static_cast<Real>(1200) * std::pow((*ex)[0],2)
115  + static_cast<Real>(2);
116  Real h22 = static_cast<Real>(200);
117  Real h12 = static_cast<Real>(-400) * (*ex)[0];
118  Real h21 = static_cast<Real>(-400) * (*ex)[0];
119 
120  Real alpha(0);
121 
122  (*ehv)[0] = (h11+alpha) * (*ev)[0] + h12 * (*ev)[1];
123  (*ehv)[1] = h21 * (*ev)[0] + (h22+alpha) * (*ev)[1];
124  }
125 #endif
126  void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
127 
128  using Teuchos::RCP;
129  RCP<const vector> ex = getVector(x);
130  RCP<const vector> ev = getVector(v);
131  RCP< vector> ehv = getVector(hv);
132 
133  Real h11 = static_cast<Real>(-400) * (*ex)[1]
134  + static_cast<Real>(1200) * std::pow((*ex)[0],2)
135  + static_cast<Real>(2);
136  Real h22 = static_cast<Real>(200);
137  Real h12 = static_cast<Real>(-400) * (*ex)[0];
138  Real h21 = static_cast<Real>(-400) * (*ex)[0];
139 
140  (*ehv)[0] = static_cast<Real>(1)/(h11*h22 - h12*h21)
141  * (h22 * (*ev)[0] - h12 * (*ev)[1]);
142  (*ehv)[1] = static_cast<Real>(1)/(h11*h22 - h12*h21)
143  * (-h21 * (*ev)[0] + h11 * (*ev)[1]);
144  }
145  };
146 
147 template<class Real>
148 void getHS2( Teuchos::RCP<Objective<Real> > &obj,
149  Teuchos::RCP<BoundConstraint<Real> > &con,
150  Teuchos::RCP<Vector<Real> > &x0,
151  Teuchos::RCP<Vector<Real> > &x ) {
152  // Problem dimension
153  int n = 2;
154 
155  // Get Initial Guess
156  Teuchos::RCP<std::vector<Real> > x0p = Teuchos::rcp(new std::vector<Real>(n,0.0));
157  (*x0p)[0] = -2.0; (*x0p)[1] = 1.0;
158  x0 = Teuchos::rcp(new StdVector<Real>(x0p));
159 
160  // Get Solution
161  Teuchos::RCP<std::vector<Real> > xp = Teuchos::rcp(new std::vector<Real>(n,0.0));
162  Real a = std::sqrt(598.0/1200.0);
163  Real b = 400.0 * std::pow(a,3.0);
164  (*xp)[0] = 2.0*a*std::cos(1.0/3.0 * std::acos(1.0/b));
165  (*xp)[1] = 1.5;
166  x = Teuchos::rcp(new StdVector<Real>(xp));
167 
168  // Instantiate Objective Function
169  obj = Teuchos::rcp(new Objective_HS2<Real>);
170 
171  // Instantiate BoundConstraint
172  Teuchos::RCP<std::vector<Real> > lp = Teuchos::rcp(new std::vector<Real>(n,0.0));
173  (*lp)[0] = ROL_NINF<Real>(); (*lp)[1] = 1.5;
174  Teuchos::RCP<Vector<Real> > l = Teuchos::rcp( new StdVector<Real>(lp) );
175  Teuchos::RCP<std::vector<Real> > up = Teuchos::rcp(new std::vector<Real>(n,0.0));
176  (*up)[0] = ROL_INF<Real>(); (*up)[1] = ROL_INF<Real>();
177  Teuchos::RCP<Vector<Real> > u = Teuchos::rcp( new StdVector<Real>(up) );
178  con = Teuchos::rcp(new BoundConstraint<Real>(l,u));
179 }
180 
181 } // End ZOO Namespace
182 } // End ROL Namespace
183 
184 #endif
Provides the interface to evaluate objective functions.
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply Hessian approximation to vector.
Contains definitions of custom data types in ROL.
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Definition: ROL_HS2.hpp:96
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:74
Vector< Real > V
Definition: ROL_HS2.hpp:70
StdVector< Real > SV
Definition: ROL_HS2.hpp:71
void invHessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply inverse Hessian approximation to vector.
Definition: ROL_HS2.hpp:126
void getHS2(Teuchos::RCP< Objective< Real > > &obj, Teuchos::RCP< BoundConstraint< Real > > &con, Teuchos::RCP< Vector< Real > > &x0, Teuchos::RCP< Vector< Real > > &x)
Definition: ROL_HS2.hpp:148
std::vector< Real > vector
Definition: ROL_HS2.hpp:69
Provides the interface to apply upper and lower bound constraints.
Teuchos::RCP< vector > getVector(V &x)
Definition: ROL_HS2.hpp:80
Real value(const Vector< Real > &x, Real &tol)
Compute value.
Definition: ROL_HS2.hpp:88
Teuchos::RCP< const vector > getVector(const V &x)
Definition: ROL_HS2.hpp:75
W. Hock and K. Schittkowski 2nd test function.
Definition: ROL_HS2.hpp:67