ROL
ROL_Powell.hpp
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2 // *****************************************************************************
3 // Rapid Optimization Library (ROL) Package
4 //
5 // Copyright 2014 NTESS and the ROL contributors.
6 // SPDX-License-Identifier: BSD-3-Clause
7 // *****************************************************************************
8 // @HEADER
9 
15 #ifndef USE_HESSVEC
16 #define USE_HESSVEC 1
17 #endif
18 
19 #ifndef ROL_POWELL_HPP
20 #define ROL_POWELL_HPP
21 
22 #include "ROL_ScaledStdVector.hpp"
23 #include "ROL_TestProblem.hpp"
24 
25 namespace ROL {
26 namespace ZOO {
27 
30 template<class Real>
31 class Objective_Powell : public Objective<Real> {
32 
33 public:
35 
36  Real value( const Vector<Real> &x, Real &tol ) {
37  ROL::Ptr<const std::vector<Real> > xp
38  = dynamic_cast<const PrimalScaledStdVector<Real>&>(x).getVector();
39 
40  Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
41  Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;
42 
43  return f1*f1+f2*f2;
44  }
45 
46  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
47  ROL::Ptr<std::vector<Real> > gp
48  = dynamic_cast<DualScaledStdVector<Real>&>(g).getVector();
49  ROL::Ptr<const std::vector<Real> > xp
50  = dynamic_cast<const PrimalScaledStdVector<Real>&>(x).getVector();
51 
52  Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
53  Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;
54 
55  Real f11 = 1.e4*(*xp)[1];
56  Real f12 = 1.e4*(*xp)[0];
57  Real f21 = -std::exp(-(*xp)[0]);
58  Real f22 = -std::exp(-(*xp)[1]);
59 
60  (*gp)[0] = 2.0*(f11*f1 + f21*f2);
61  (*gp)[1] = 2.0*(f12*f1 + f22*f2);
62  }
63 #if USE_HESSVEC
64  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
65  ROL::Ptr<std::vector<Real> > hvp
66  = dynamic_cast<DualScaledStdVector<Real>&>(hv).getVector();
67  ROL::Ptr<const std::vector<Real> > vp
68  = dynamic_cast<const PrimalScaledStdVector<Real>&>(v).getVector();
69  ROL::Ptr<const std::vector<Real> > xp
70  = dynamic_cast<const PrimalScaledStdVector<Real>&>(x).getVector();
71 
72  Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
73  Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;
74 
75  Real f11 = 1.e4*(*xp)[1];
76  Real f12 = 1.e4*(*xp)[0];
77  Real f21 = -std::exp(-(*xp)[0]);
78  Real f22 = -std::exp(-(*xp)[1]);
79 
80  Real f111 = 0.0;
81  Real f112 = 1.e4;
82  Real f121 = 1.e4;
83  Real f122 = 0.0;
84  Real f211 = std::exp(-(*xp)[0]);
85  Real f212 = 0.0;
86  Real f221 = 0.0;
87  Real f222 = std::exp(-(*xp)[1]);
88 
89  Real h11 = 2.0*(f111*f1 + f11*f11) + 2.0*(f211*f2 + f21*f21);
90  Real h12 = 2.0*(f112*f1 + f11*f12) + 2.0*(f212*f2 + f21*f22);
91  Real h21 = 2.0*(f121*f1 + f12*f11) + 2.0*(f221*f2 + f22*f21);
92  Real h22 = 2.0*(f122*f1 + f12*f12) + 2.0*(f222*f2 + f22*f22);
93 
94  (*hvp)[0] = h11*(*vp)[0] + h12*(*vp)[1];
95  (*hvp)[1] = h21*(*vp)[0] + h22*(*vp)[1];
96  }
97 #endif
98  void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
99  ROL::Ptr<std::vector<Real> > hvp
100  = dynamic_cast<PrimalScaledStdVector<Real>&>(hv).getVector();
101  ROL::Ptr<const std::vector<Real> > vp
102  = dynamic_cast<const DualScaledStdVector<Real>&>(v).getVector();
103  ROL::Ptr<const std::vector<Real> > xp
104  = dynamic_cast<const PrimalScaledStdVector<Real>&>(x).getVector();
105 
106  Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
107  Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;
108 
109  Real f11 = 1.e4*(*xp)[1];
110  Real f12 = 1.e4*(*xp)[0];
111  Real f21 = -std::exp(-(*xp)[0]);
112  Real f22 = -std::exp(-(*xp)[1]);
113 
114  Real f111 = 0.0;
115  Real f112 = 1.e4;
116  Real f121 = 1.e4;
117  Real f122 = 0.0;
118  Real f211 = std::exp(-(*xp)[0]);
119  Real f212 = 0.0;
120  Real f221 = 0.0;
121  Real f222 = std::exp(-(*xp)[1]);
122 
123  Real h11 = 2.0*(f111*f1 + f11*f11) + 2.0*(f211*f2 + f21*f21);
124  Real h12 = 2.0*(f112*f1 + f11*f12) + 2.0*(f212*f2 + f21*f22);
125  Real h21 = 2.0*(f121*f1 + f21*f11) + 2.0*(f221*f2 + f22*f21);
126  Real h22 = 2.0*(f122*f1 + f12*f12) + 2.0*(f222*f2 + f22*f22);
127 
128  (*hvp)[0] = (1.0/(h11*h22-h12*h21))*( h22*(*vp)[0] - h21*(*vp)[1]);
129  (*hvp)[1] = (1.0/(h11*h22-h12*h21))*(-h12*(*vp)[0] + h11*(*vp)[1]);
130  }
131 };
132 
133 template<class Real>
134 class getPowell : public TestProblem<Real> {
135 private:
136  ROL::Ptr<std::vector<Real> > scale_;
137 
138 public:
139  getPowell(void) {
140  // Get problem scaling
141  scale_ = ROL::makePtr<std::vector<Real>>(2,0.0);
142  (*scale_)[0] = 1.e10; (*scale_)[1] = 1.e-2;
143  }
144 
145  Ptr<Objective<Real>> getObjective(void) const {
146  // Instantiate Objective Function
147  return ROL::makePtr<Objective_Powell<Real>>();
148  }
149 
150  Ptr<Vector<Real>> getInitialGuess(void) const {
151  // Problem dimension
152  int n = 2;
153  // Get Initial Guess
154  ROL::Ptr<std::vector<Real> > x0p = ROL::makePtr<std::vector<Real>>(n,0.0);
155  (*x0p)[0] = 0.0; (*x0p)[1] = 1.0;
156  return ROL::makePtr<PrimalScaledStdVector<Real>>(x0p,scale_);
157  }
158 
159  Ptr<Vector<Real>> getSolution(const int i = 0) const {
160  // Problem dimension
161  int n = 2;
162  // Get Solution: (*xp)[0] = 1.0981770261368074e-05;
163  ROL::Ptr<std::vector<Real> > xp = ROL::makePtr<std::vector<Real>>(n,0.0);
164  (*xp)[0] = 1.098e-05; (*xp)[1] = 9.106;
165  return ROL::makePtr<PrimalScaledStdVector<Real>>(xp,scale_);
166  }
167 };
168 
169 } // End ZOO Namespace
170 } // End ROL Namespace
171 
172 #endif
Provides the interface to evaluate objective functions.
Real value(const Vector< Real > &x, Real &tol)
Compute value.
Definition: ROL_Powell.hpp:36
ROL::Ptr< std::vector< Real > > scale_
Definition: ROL_Powell.hpp:136
Provides the std::vector implementation of the ROL::Vector interface that handles scalings in the inn...
Powell&#39;s badly scaled function.
Definition: ROL_Powell.hpp:31
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply Hessian approximation to vector.
Ptr< Vector< Real > > getSolution(const int i=0) const
Definition: ROL_Powell.hpp:159
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:46
Contains definitions of test objective functions.
Ptr< Vector< Real > > getInitialGuess(void) const
Definition: ROL_Powell.hpp:150
Provides the std::vector implementation of the ROL::Vector interface that handles scalings in the inn...
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Definition: ROL_Powell.hpp:46
void invHessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply inverse Hessian approximation to vector.
Definition: ROL_Powell.hpp:98
Ptr< Objective< Real > > getObjective(void) const
Definition: ROL_Powell.hpp:145