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// Copyright (C) 2005, 2006 International Business Machines and others.
// All Rights Reserved.
// This code is published under the Eclipse Public License.
//
// Authors: Andreas Waechter IBM 2005-10-127
#include "LuksanVlcek2.hpp"
#include <cmath>
#include <cstdio>
using namespace Ipopt;
LuksanVlcek2::LuksanVlcek2(
Number g_l,
Number g_u
)
: g_l_(g_l),
g_u_(g_u)
{ }
bool LuksanVlcek2::InitializeProblem(
Index N
)
{
N_ = N;
if( N_ <= 13 || 2 * (N_ / 2) != N_ )
{
printf("N needs to be at least 14 and even.\n");
return false;
}
return true;
}
// returns the size of the problem
bool LuksanVlcek2::get_nlp_info(
Index& n,
Index& m,
Index& nnz_jac_g,
Index& nnz_h_lag,
IndexStyleEnum& index_style
)
{
// The problem described in LuksanVlcek2.hpp has 4 variables, x[0]
// through x[3]
n = N_ + 2;
m = N_ - 7;
nnz_jac_g = 25 + (m - 5) * 8;
nnz_h_lag = n + N_ + 1;
// use the C style numbering of matrix indices (starting at 0)
index_style = TNLP::C_STYLE;
return true;
}
// returns the variable bounds
bool LuksanVlcek2::get_bounds_info(
Index n,
Number* x_l,
Number* x_u,
Index m,
Number* g_l,
Number* g_u
)
{
// none of the variables have bounds
for( Index i = 0; i < n; i++ )
{
x_l[i] = -1e20;
x_u[i] = 1e20;
}
// Set the bounds for the constraints
for( Index i = 0; i < m; i++ )
{
g_l[i] = g_l_;
g_u[i] = g_u_;
}
return true;
}
// returns the initial point for the problem
bool LuksanVlcek2::get_starting_point(
Index n,
bool init_x,
Number* x,
bool init_z,
Number* /*z_L*/,
Number* /*z_U*/,
Index /*m*/,
bool init_lambda,
Number* /*lambda*/
)
{
if( !init_x || init_z || init_lambda )
{
return false;
}
// set the starting point
for( Index i = 0; i < n / 2; i++ )
{
x[2 * i] = -2.;
x[2 * i + 1] = 1.;
}
return true;
}
// returns the value of the objective function
bool LuksanVlcek2::eval_f(
Index /*n*/,
const Number* x,
bool /*new_x*/,
Number& obj_value
)
{
obj_value = 0.;
for( Index i = 0; i < N_ / 2; i++ )
{
Number a1 = x[2 * i] * x[2 * i] - x[2 * i + 1];
Number a2 = x[2 * i] - 1.;
Number a3 = x[2 * i + 2] * x[2 * i + 2] - x[2 * i + 3];
Number a4 = x[2 * i + 2] - 1.;
Number a5 = x[2 * i + 1] + x[2 * i + 3] - 2.;
Number a6 = x[2 * i + 1] - x[2 * i + 3];
obj_value += 100. * a1 * a1 + a2 * a2 + 90. * a3 * a3 + a4 * a4 + 10. * a5 * a5 + .1 * a6 * a6;
}
return true;
}
// return the gradient of the objective function grad_{x} f(x)
bool LuksanVlcek2::eval_grad_f(
Index /*n*/,
const Number* x,
bool /*new_x*/,
Number* grad_f
)
{
grad_f[0] = 0.;
grad_f[1] = 0.;
for( Index i = 0; i < N_ / 2; i++ )
{
grad_f[2 * i] += 400. * x[2 * i] * (x[2 * i] * x[2 * i] - x[2 * i + 1]) + 2. * (x[2 * i] - 1.);
grad_f[2 * i + 1] += -200. * (x[2 * i] * x[2 * i] - x[2 * i + 1]) + 20 * (x[2 * i + 1] + x[2 * i + 3] - 2.)
+ 0.2 * (x[2 * i + 1] - x[2 * i + 3]);
grad_f[2 * i + 2] = 360. * x[2 * i + 2] * (x[2 * i + 2] * x[2 * i + 2] - x[2 * i + 3]) + 2. * (x[2 * i + 2] - 1.);
grad_f[2 * i + 3] = -180. * (x[2 * i + 2] * x[2 * i + 2] - x[2 * i + 3])
+ 20. * (x[2 * i + 1] + x[2 * i + 3] - 2.) - 0.2 * (x[2 * i + 1] - x[2 * i + 3]);
}
return true;
}
// return the value of the constraints: g(x)
bool LuksanVlcek2::eval_g(
Index /*n*/,
const Number* x,
bool /*new_x*/,
Index /*m*/,
Number* g
)
{
for( Index i = 0; i < N_ - 7; i++ )
{
g[i] = (2. + 5. * x[i + 5] * x[i + 5]) * x[i + 5] + 1.;
for( Index k = Max(Index(0), i - 5); k <= i + 1; k++ )
{
g[i] += x[k] * (x[k] + 1.);
}
}
return true;
}
// return the structure or values of the Jacobian
bool LuksanVlcek2::eval_jac_g(
Index /*n*/,
const Number* x,
bool /*new_x*/,
Index /*m*/,
Index nele_jac,
Index* iRow,
Index* jCol,
Number* values
)
{
if( values == NULL )
{
// return the structure of the jacobian
Index ijac = 0;
for( Index i = 0; i < N_ - 7; i++ )
{
for( Index k = Max(Index(0), i - 5); k <= i + 1; k++ )
{
iRow[ijac] = i;
jCol[ijac] = k;
ijac++;
}
iRow[ijac] = i;
jCol[ijac] = i + 5;
ijac++;
}
DBG_ASSERT(ijac == nele_jac);
(void) nele_jac;
}
else
{
// return the values of the jacobian of the constraints
Index ijac = 0;
for( Index i = 0; i < N_ - 7; i++ )
{
for( Index k = Max(Index(0), i - 5); k <= i + 1; k++ )
{
values[ijac] = 2. * x[k] + 1.;
ijac++;
}
values[ijac] = 2. + 15. * x[i + 5] * x[i + 5];
ijac++;
}
}
return true;
}
//return the structure or values of the Hessian
bool LuksanVlcek2::eval_h(
Index n,
const Number* x,
bool /*new_x*/,
Number obj_factor,
Index /*m*/,
const Number* lambda,
bool /*new_lambda*/,
Index nele_hess,
Index* iRow,
Index* jCol,
Number* values
)
{
if( values == NULL )
{
Index ihes = 0;
// First the diagonal elements
for( Index i = 0; i < n; i++ )
{
iRow[ihes] = i;
jCol[ihes] = i;
ihes++;
}
// And now the off-diagonal elements
for( Index i = 0; i < N_ / 2; i++ )
{
iRow[ihes] = 2 * i;
jCol[ihes] = 2 * i + 1;
ihes++;
iRow[ihes] = 2 * i + 1;
jCol[ihes] = 2 * i + 3;
ihes++;
}
iRow[ihes] = n - 2;
jCol[ihes] = n - 1;
DBG_DO(ihes++);
DBG_ASSERT(ihes == nele_hess);
(void) nele_hess;
}
else
{
// First we take care of the diagonal elements coming from the
// objective function
values[0] = 0.;
values[1] = 0.;
for( Index i = 0; i < N_ / 2; i++ )
{
values[2 * i] += obj_factor * (1200. * x[2 * i] * x[2 * i] - 400. * x[2 * i + 1] + 2.);
values[2 * i + 1] += obj_factor * 220.2;
values[2 * i + 2] = obj_factor * (1080. * x[2 * i + 2] * x[2 * i + 2] - 360 * x[2 * i + 3] + 2.);
values[2 * i + 3] = obj_factor * 200.2;
}
// Now we take care of the off-diagonal elements coming from the
// objective function
Index ihes = n;
values[ihes] = 0.;
for( Index i = 0; i < N_ / 2; i++ )
{
values[ihes] += obj_factor * (-400. * x[2 * i]);
ihes++;
values[ihes] = obj_factor * 19.8;
ihes++;
values[ihes] = obj_factor * (-360. * x[2 * i + 2]);
}
// Ok, now the diagonal elements from the constraints
for( Index i = 0; i < N_ - 7; i++ )
{
for( Index k = Max(Index(0), i - 5); k <= i + 1; k++ )
{
values[k] += lambda[i] * 2.;
}
values[i + 5] += lambda[i] * 30. * x[i + 5];
}
}
return true;
}
void LuksanVlcek2::finalize_solution(
SolverReturn /*status*/,
Index /*n*/,
const Number* /*x*/,
const Number* /*z_L*/,
const Number* /*z_U*/,
Index /*m*/,
const Number* /*g*/,
const Number* /*lambda*/,
Number /*obj_value*/,
const IpoptData* /*ip_data*/,
IpoptCalculatedQuantities* /*ip_cq*/
)
{ }
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