ROL
test_11.hpp
Go to the documentation of this file.
1// @HEADER
2// ************************************************************************
3//
4// Rapid Optimization Library (ROL) Package
5// Copyright (2014) Sandia Corporation
6//
7// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
8// license for use of this work by or on behalf of the U.S. Government.
9//
10// Redistribution and use in source and binary forms, with or without
11// modification, are permitted provided that the following conditions are
12// met:
13//
14// 1. Redistributions of source code must retain the above copyright
15// notice, this list of conditions and the following disclaimer.
16//
17// 2. Redistributions in binary form must reproduce the above copyright
18// notice, this list of conditions and the following disclaimer in the
19// documentation and/or other materials provided with the distribution.
20//
21// 3. Neither the name of the Corporation nor the names of the
22// contributors may be used to endorse or promote products derived from
23// this software without specific prior written permission.
24//
25// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
26// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
28// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
29// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
33// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
34// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36//
37// Questions? Contact lead developers:
38// Drew Kouri (dpkouri@sandia.gov) and
39// Denis Ridzal (dridzal@sandia.gov)
40//
41// ************************************************************************
42// @HEADER
43
44/* \file test_11.hpp
45 \brief Verify that the Coleman-Li Model function produces the
46 correct values for a test problem
47
48 \f[ \min_x f(x) = \frac{1}{2}(x_1^2+2x_2^2),\quad x_1 \geq 1,\; x_2 <= -1 \f]
49
50 The gradient is
51 \f[ \nabla f(x) = (x_1,2 x_2 ) \f]
52
53 and the Hessian is
54 \[f \nabla^2 f(x) = \begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix} \f]
55
56 The minimizer is \f$ x^\ast = (1,-1)\f$
57
58 For feasible \f$x\f$, the Coleman-Li quantities of interest are
59
60 \f[ v_1 = x_1 - 1,\quad v_2 = -1 - x_2 \f]
61 \f[ D^{-1} = \begin{pmatrix} \sqrt{|x_1-1|} & 0 \\ 0 & \sqrt{|x_2+1|} \end{pmatrix} \f]
62 \f[ J=\begin{pmatrix} 1 & -1 \end{pmatrix} \f]
63 \f[ \hat M_k = \begin{pmatrix} |x_1-1|^2+|x_1| & 0 \\
64 0 & |x_2+1|^2+2|x_2| \end{pmatrix} \f]
65
66
67*/
68
69#include "ROL_Objective.hpp"
70#include "ROL_StdVector.hpp"
71
72template<class Real>
73class CLTestObjective : public ROL::Objective<Real> {
74
75
76public:
77
78 Real value( const ROL::Vector<Real> &x, Real &tol ) {
79 ROL::Ptr<const std::vector<Real> > xp =
80 dynamic_cast<const ROL::StdVector<Real>&>(x).getVector();
81 return 0.5*((*xp)[0]*(*xp)[0] + 2*(*xp)[1]*(*xp)[1]);
82 }
83
84 void gradient( ROL::Vector<Real> &g, const ROL::Vector<Real> &x, Real &tol ) {
85 ROL::Ptr<std::vector<Real> > gp =
86 dynamic_cast<ROL::StdVector<Real>&>(g).getVector();
87 ROL::Ptr<const std::vector<Real> > xp =
88 dynamic_cast<const ROL::StdVector<Real>&>(x).getVector();
89 (*gp)[0] = (*xp)[0];
90 (*gp)[1] = 2*(*xp)[1];
91 }
92
94 const ROL::Vector<Real> &v,
95 const ROL::Vector<Real> &x,
96 Real &tol ) {
97 ROL::Ptr<std::vector<Real> > hvp =
98 dynamic_cast<ROL::StdVector<Real>&>(hv).getVector();
99 ROL::Ptr<const std::vector<Real> > vp =
100 dynamic_cast<const ROL::StdVector<Real>&>(v).getVector();
101 (*hvp)[0] = (*vp)[0];
102 (*hvp)[1] = 2*(*vp)[1];
103 }
104
105}; // CLTestObjective
106
107template<class Real>
108class CLExactModel : public ROL::Objective<Real> {
109
110ROL::Ptr<std::vector<Real> > x_;
111const ROL::Ptr<const std::vector<Real> > l_;
112const ROL::Ptr<const std::vector<Real> > u_;
113ROL::Ptr<std::vector<Real> > g_;
114ROL::Ptr<std::vector<Real> > di_;
115ROL::Ptr<std::vector<Real> > j_;
116ROL::Ptr<ROL::Objective<Real> > obj_;
117
118public:
119
120 CLExactModel( ROL::Ptr<std::vector<Real> > &xp,
121 const ROL::Ptr<const std::vector<Real> > &lp,
122 const ROL::Ptr<const std::vector<Real> > &up ) :
123 x_(xp), l_(lp), u_(up) {
124 g_ = ROL::makePtr<std::vector<double>(x_->size>());
125 di_ = ROL::makePtr<std::vector<double>(x_->size>());
126 j_ = ROL::makePtr<std::vector<double>(x_->size>());
127
128
129 obj_ = ROL::makePtr<CLTestObjective<Real>>();
130
133 Real tol = std::sqrt(ROL::ROL_EPSILON<Real>());
134 obj_->gradient(g,x,tol);
135
136 std::vector<Real> v(2);
137
138 for(int i=0; i<2;++i) {
139 (*j_)[i] = 0;
140 // Case (i)
141 if( (*g_)[i]<0 && (*u_)[i] < ROL::ROL_INF<Real>() ) {
142 v[i] = (*u_)[i]-(*x_)[i];
143 (*j_)[i] = -1;
144 }
145 // Case (ii)
146 else if( (*g_)[i]>=0 && (*l_)[i] > ROL::ROL_NINF<Real>() ) {
147 v[i] = (*x_)[i] - (*l_)[i];
148 (*j_)[i] = 1;
149 }
150 // Case (iii)
151 else if( (*g_)[i]<=0 && (*u_)[i] == ROL::ROL_INF<Real>() ) {
152 v[i] = -1;
153 }
154 // Case (iv)
155 else {
156 v[i] = 1;
157 }
158 (*di_)[i] = std::sqrt(std::abs(v[i]));
159 }
160
161
162 std::cout << "x[0] = " << (*x_)[0] << std::endl;
163 std::cout << "x[1] = " << (*x_)[1] << std::endl;
164 std::cout << "g[0] = " << (*g_)[0] << std::endl;
165 std::cout << "g[0] = " << (*g_)[1] << std::endl;
166 std::cout << "di[0] = " << (*di_)[0] << std::endl;
167 std::cout << "di[1] = " << (*di_)[1] << std::endl;
168
169 }
170
171 void update( const ROL::Vector<Real> &x, bool flag = true, int iter=-1 ) {
172 ROL::Ptr<const std::vector<Real> > xc =
173 dynamic_cast<const ROL::StdVector<Real>&>(x).getVector();
174 (*x_)[0] = (*xc)[0];
175 (*x_)[1] = (*xc)[1];
176
177 std::vector<Real> v(2);
179 Real tol = std::sqrt(ROL::ROL_EPSILON<Real>());
180 obj_->gradient(g,x,tol);
181
182 for(int i=0; i<2;++i) {
183 (*j_)[i] = 0;
184 // Case (i)
185 if( (*g_)[i]<0 && (*u_)[i] < ROL::ROL_INF<Real>() ) {
186 v[i] = (*u_)[i]-(*x_)[i];
187 (*j_)[i] = -1;
188 }
189 // Case (ii)
190 else if( (*g_)[i]>=0 && (*l_)[i] > ROL::ROL_NINF<Real>() ) {
191 v[i] = (*x_)[i] - (*l_)[i];
192 (*j_)[i] = 1;
193 }
194 // Case (iii)
195 else if( (*g_)[i]<=0 && (*u_)[i] == ROL::ROL_INF<Real>() ) {
196 v[i] = -1;
197 }
198 // Case (iv)
199 else {
200 v[i] = 1;
201 }
202 (*di_)[i] = std::sqrt(std::abs(v[i]));
203 }
204
205 std::cout << "x[0] = " << (*x_)[0] << std::endl;
206 std::cout << "x[1] = " << (*x_)[1] << std::endl;
207 std::cout << "g[0] = " << (*g_)[0] << std::endl;
208 std::cout << "g[0] = " << (*g_)[1] << std::endl;
209 std::cout << "di[0] = " << (*di_)[0] << std::endl;
210 std::cout << "di[1] = " << (*di_)[1] << std::endl;
211 }
212
213 Real value( const ROL::Vector<Real> &s, Real &tol ) {
214 ROL::Ptr<const std::vector<Real> > sp =
215 dynamic_cast<const ROL::StdVector<Real>&>(s).getVector();
216
217 ROL::Ptr<ROL::Vector<Real> > y = s.clone();
218 hessVec(*y,s,s,tol);
219 Real result = 0.5*y->dot(s);
220 result += (*di_)[0]*(*g_)[0]*(*sp)[0];
221 result += (*di_)[1]*(*g_)[1]*(*sp)[1];
222 return result;
223 }
224
225 void gradient( ROL::Vector<Real> &g, const ROL::Vector<Real> &s, Real &tol ) {
226 ROL::Ptr<std::vector<Real> > gp =
227 dynamic_cast<ROL::StdVector<Real>&>(g).getVector();
228 hessVec(g,s,s,tol);
229
230 (*gp)[0] += (*di_)[0]*(*g_)[0];
231 (*gp)[1] += (*di_)[1]*(*g_)[1];
232 }
233
235 const ROL::Vector<Real> &v,
236 const ROL::Vector<Real> &s,
237 Real &tol ) {
238
239 ROL::Ptr<std::vector<Real> > hvp =
240 dynamic_cast<ROL::StdVector<Real>&>(hv).getVector();
241 ROL::Ptr<const std::vector<Real> > vp =
242 dynamic_cast<const ROL::StdVector<Real>&>(v).getVector();
243
244 obj_->hessVec(hv,v,s,tol);
245
246 for(int i=0; i<2; ++i) {
247 (*hvp)[i] *= (*di_)[i]*(*di_)[i];
248 (*hvp)[i] += (*g_)[i]*(*j_)[i]*(*vp)[i];
249 }
250
251 }
252
253
254}; // CLExactModel
255
256
257
258
ROL::Ptr< std::vector< Real > > j_
Definition test_11.hpp:115
ROL::Ptr< ROL::Objective< Real > > obj_
Definition test_11.hpp:116
void update(const ROL::Vector< Real > &x, bool flag=true, int iter=-1)
Update objective function.
Definition test_11.hpp:171
void gradient(ROL::Vector< Real > &g, const ROL::Vector< Real > &s, Real &tol)
Compute gradient.
Definition test_11.hpp:225
const ROL::Ptr< const std::vector< Real > > l_
Definition test_11.hpp:111
ROL::Ptr< std::vector< Real > > x_
Definition test_11.hpp:110
ROL::Ptr< std::vector< Real > > di_
Definition test_11.hpp:114
ROL::Ptr< std::vector< Real > > g_
Definition test_11.hpp:113
const ROL::Ptr< const std::vector< Real > > u_
Definition test_11.hpp:112
void hessVec(ROL::Vector< Real > &hv, const ROL::Vector< Real > &v, const ROL::Vector< Real > &s, Real &tol)
Apply Hessian approximation to vector.
Definition test_11.hpp:234
Real value(const ROL::Vector< Real > &s, Real &tol)
Compute value.
Definition test_11.hpp:213
CLExactModel(ROL::Ptr< std::vector< Real > > &xp, const ROL::Ptr< const std::vector< Real > > &lp, const ROL::Ptr< const std::vector< Real > > &up)
Definition test_11.hpp:120
void gradient(ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real &tol)
Compute gradient.
Definition test_11.hpp:84
void hessVec(ROL::Vector< Real > &hv, const ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real &tol)
Apply Hessian approximation to vector.
Definition test_11.hpp:93
Real value(const ROL::Vector< Real > &x, Real &tol)
Compute value.
Definition test_11.hpp:78
Provides the interface to evaluate objective functions.
Provides the ROL::Vector interface for scalar values, to be used, for example, with scalar constraint...
Defines the linear algebra or vector space interface.
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.