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/* Copyright (C) 2007 VRTech Industrial Technologies - www.vrtech.com.br.
* Copyright (C) 2007 Tong Kewei, Beihang University, - www.buaa.edu.cn.
* All Rights Reserved.
* This code is published under the Eclipse Public License.
*/
/** Implementation of Example 5.1 from "Sparse and Parially Separable Test Problems for Unconstrained and Equality Constrained Optimization" by L. Luksan and J. Vlcek.
*
* This code is based on an Ipopt example file with same name.
*
* @author Rafael de Pelegrini Soares, Tong Kewei
*/
public class LuksanVlcek1 extends Scalable
{
/** Constructor.
*
* Here, gl and gu are the bounds for the constraints.
* The original formulation is obtained by setting gl and gu to zero.
* Using gl lower than gu allows the obtain a problem formulation with inequality
* constraints.
*/
public LuksanVlcek1(
String name,
double gl,
double gu)
{
super(name, gl, gu);
}
@Override
public boolean initialize(
int n)
{
if( n <= 2 )
{
System.out.print("N needs to be at least 3.\n");
return false;
}
// The problem described in LuksanVlcek1.hpp has 4 variables, x[0] through x[3]
this.n = n;
m = n - 2;
nnz_jac_g = m * 3;
nnz_h_lag = n + n - 1;
// use the C style numbering of matrix indices (starting at 0)
index_style = C_STYLE;
// none of the variables have bounds
x_l = new double[n];
x_u = new double[n];
for( int i = 0; i < n; ++i )
{
x_l[i] = -1e20;
x_u[i] = 1e20;
}
// Set the bounds for the constraints
g_l = new double[m];
g_u = new double[m];
for( int i = 0; i < m; ++i )
{
g_l[i] = gl;
g_u[i] = gu;
}
// set the starting point
x = new double[n];
for( int i = 0; i < n / 2; ++i )
{
x[2 * i ] = -1.2;
x[2 * i + 1] = 1.0;
}
if (n % 2 == 1)
{
x[n - 1] = -1.2;
}
return true;
}
protected boolean get_bounds_info(
int n,
double[] x_l,
double[] x_u,
int m,
double[] g_l,
double[] g_u)
{
// none of the variables have bounds
for( int i = 0; i < n; ++i )
{
x_l[i] = -1e20;
x_u[i] = 1e20;
}
// Set the bounds for the constraints
for( int i = 0; i < m; ++i )
{
g_l[i] = gl;
g_u[i] = gu;
}
return true;
}
protected boolean get_starting_point(
int n,
boolean init_x,
double[] x,
boolean init_z,
double[] z_L,
double[] z_U,
int m,
boolean init_lambda,
double[] lambda)
{
for( int i = 0; i < n / 2; ++i )
{
x[2 * i ] = -1.2;
x[2 * i + 1] = 1.0;
}
if (n % 2 == 1)
{
x[n - 1] = -1.2;
}
return true;
}
@Override
protected boolean eval_f(
int n,
double[] x,
boolean new_x,
double[] obj_value)
{
obj_value[0] = 0.0;
for( int i = 0; i < n - 1; ++i )
{
double a1 = x[i] * x[i] - x[i + 1];
double a2 = x[i] - 1.0;
obj_value[0] += 100.0 * a1 * a1 + a2 * a2;
}
return true;
}
@Override
protected boolean eval_g(
int n,
double[] x,
boolean new_x,
int m,
double[] g)
{
for( int i = 0; i < n - 2; ++i )
g[i] = 3.0 * Math.pow(x[i + 1], 3.0)
+ 2.0 * x[i + 2]
- 5.0
+ Math.sin(x[i + 1] - x[i + 2]) * Math.sin(x[i + 1] + x[i + 2])
+ 4.0 * x[i + 1]
- x[i] * Math.exp(x[i] - x[i + 1])
- 3.0;
return true;
}
@Override
protected boolean eval_grad_f(
int n,
double[] x,
boolean new_x,
double[] grad_f)
{
grad_f[0] = 0.0;
for( int i = 0; i < n - 1; ++i )
{
grad_f[i] += 400.0 * x[i] * (x[i] * x[i] - x[i + 1]) + 2.0 * (x[i] - 1.0);
grad_f[i + 1] = -200.0 * (x[i] * x[i] - x[i + 1]);
}
return true;
}
@Override
protected boolean eval_jac_g(
int n,
double[] x,
boolean new_x,
int m,
int nele_jac,
int[] iRow,
int[] jCol,
double[] values)
{
if( values == null )
{
// return the structure of the jacobian
int ijac = 0;
for( int i = 0; i < n - 2; ++i )
{
iRow[ijac] = i;
jCol[ijac] = i;
ijac++;
iRow[ijac] = i;
jCol[ijac] = i + 1;
ijac++;
iRow[ijac] = i;
jCol[ijac] = i + 2;
ijac++;
}
}
else
{
// return the values of the jacobian of the constraints
int ijac = 0;
for( int i = 0; i < n - 2; ++i )
{
// x[i]
values[ijac] = -(1.0 + x[i]) * Math.exp(x[i] - x[i + 1]);
ijac++;
// x[i+1]
values[ijac] = 9.0 * x[i + 1] * x[i + 1]
+ Math.cos(x[i + 1] - x[i + 2]) * Math.sin(x[i + 1] + x[i + 2])
+ Math.sin(x[i + 1] - x[i + 2]) * Math.cos(x[i + 1] + x[i + 2])
+ 4.0
+ x[i] * Math.exp(x[i] - x[i + 1]);
ijac++;
// x[i+2]
values[ijac] = 2.0
- Math.cos(x[i + 1] - x[i + 2]) * Math.sin(x[i + 1] + x[i + 2])
+ Math.sin(x[i + 1] - x[i + 2]) * Math.cos(x[i + 1] + x[i + 2]);
ijac++;
}
}
return true;
}
@Override
protected boolean eval_h(
int n,
double[] x,
boolean new_x,
double obj_factor,
int m,
double[] lambda,
boolean new_lambda,
int nele_hess,
int[] iRow,
int[] jCol,
double[] values)
{
if( values == null )
{
int ihes = 0;
for( int i = 0; i < n; ++i )
{
iRow[ihes] = i;
jCol[ihes] = i;
++ihes;
if( i < n - 1 )
{
iRow[ihes] = i;
jCol[ihes] = i + 1;
ihes++;
}
}
assert ihes == nele_hess;
}
else
{
int ihes = 0;
for( int i = 0; i < n; ++i )
{
// x[i],x[i]
if( i < n - 1 )
{
values[ihes] = obj_factor * (2.0 + 400.0 * (3.0 * x[i] * x[i] - x[i + 1]));
if (i < n - 2)
{
values[ihes] -= lambda[i] * (2.0 + x[i]) * Math.exp(x[i] - x[i + 1]);
}
}
else
{
values[ihes] = 0.;
}
if( i > 0 )
{
// x[i+1]x[i+1]
values[ihes] += obj_factor * 200.0;
if( i < n - 1 )
values[ihes] += lambda[i - 1] * (18.0 * x[i]
- 2.0 * Math.sin(x[i] - x[i + 1]) * Math.sin(x[i] + x[i + 1])
+ 2.0 * Math.cos(x[i] - x[i + 1]) * Math.cos(x[i] + x[i + 1])
- x[i - 1] * Math.exp(x[i - 1] - x[i]));
}
if( i > 1 )
// x[i+2]x[i+2]
values[ihes] += lambda[i - 2] * (-2.0 * Math.sin(x[i - 1] - x[i]) * Math.sin(x[i - 1] + x[i])
- 2.0 * Math.cos(x[i - 1] - x[i]) * Math.cos(x[i - 1] + x[i]));
ihes++;
if( i < n - 1 )
{
// x[i],x[i+1]
values[ihes] = obj_factor * (-400.0) * x[i];
if( i < n - 2 )
{
values[ihes] += lambda[i] * (1.0 + x[i]) * Math.exp(x[i] - x[i + 1]);
}
/*
* if (i>0) { // x[i+1],x[i+2] values[ihes] += lambda[i-1]*(
* sin(x[i]-x[i+1])*sin(x[i]+x[i+1]) +
* cos(x[i]-x[i+1])*cos(x[i]+x[i+1]) -
* cos(x[i]-x[i+1])*cos(x[i]+x[i+1]) -
* sin(x[i]-x[i+1])*sin(x[i]+x[i+1]) ); }
*/
ihes++;
}
}
assert ihes == nele_hess;
}
return true;
}
}
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