public void ConstructorTest10()
{
/// This problem is taken from page 415 of Luenberger's book Applied
/// Nonlinear Programming. It is to maximize the area of a hexagon of
/// unit diameter.
///
var function = new NonlinearObjectiveFunction(9, x =>
-0.5 * (x[0] * x[3] - x[1] * x[2] + x[2] * x[8]
- x[4] * x[8] + x[4] * x[7] - x[5] * x[6]));
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(9, x => 1.0 - x[2] * x[2] - x[3] * x[3]),
new NonlinearConstraint(9, x => 1.0 - x[8] * x[8]),
new NonlinearConstraint(9, x => 1.0 - x[4] * x[4] - x[5] * x[5]),
new NonlinearConstraint(9, x => 1.0 - x[0] * x[0] - Math.Pow(x[1] - x[8], 2.0)),
new NonlinearConstraint(9, x => 1.0 - Math.Pow(x[0] - x[4], 2.0) - Math.Pow(x[1] - x[5], 2.0)),
new NonlinearConstraint(9, x => 1.0 - Math.Pow(x[0] - x[6], 2.0) - Math.Pow(x[1] - x[7], 2.0)),
new NonlinearConstraint(9, x => 1.0 - Math.Pow(x[2] - x[4], 2.0) - Math.Pow(x[3] - x[5], 2.0)),
new NonlinearConstraint(9, x => 1.0 - Math.Pow(x[2] - x[6], 2.0) - Math.Pow(x[3] - x[7], 2.0)),
new NonlinearConstraint(9, x => 1.0 - x[6] * x[6] - Math.Pow(x[7] - x[8], 2.0)),
new NonlinearConstraint(9, x => x[0] * x[3] - x[1] * x[2]),
new NonlinearConstraint(9, x => x[2] * x[8]),
new NonlinearConstraint(9, x => -x[4] * x[8]),
new NonlinearConstraint(9, x => x[4] * x[7] - x[5] * x[6]),
new NonlinearConstraint(9, x => x[8]),
};
Cobyla cobyla = new Cobyla(function, constraints);
for (int i = 0; i < cobyla.Solution.Length; i++)
cobyla.Solution[i] = 1;
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
double[] expected =
{
0.688341, 0.725387, -0.284033, 0.958814, 0.688341, 0.725387, -0.284033, 0.958814, 0.0
};
for (int i = 0; i < expected.Length; i++)
Assert.AreEqual(expected[i], cobyla.Solution[i], 1e-2);
Assert.AreEqual(-0.86602540378486847, minimum, 1e-10);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
