public void solve_vectors()
{
#region doc_vector
// Suppose we would like to minimize the following function:
//
// f(x,y) = min 100(y-x²)²+(1-x)²
//
// Subject to the constraints
//
// x >= 0 (x must be positive)
// y >= 0 (y must be positive)
//
// Now, we can create an objective function using vectors
var f = new NonlinearObjectiveFunction(numberOfVariables: 2,
// This is the objective function: f(x,y) = min 100(y-x²)²+(1-x)²
function: (x) => 100 * Math.Pow(x[1] - x[0] * x[0], 2) + Math.Pow(1 - x[0], 2),
// And this is the vector gradient for the same function:
gradient: (x) => new[]
{
2 * (200 * Math.Pow(x[0], 3) - 200 * x[0] * x[1] + x[0] - 1), // df/dx = 2(200x³-200xy+x-1)
200 * (x[1] - x[0] * x[0]) // df/dy = 200(y-x²)
}
);
// As before, we state the constraints. However, to illustrate the flexibility
// of the AugmentedLagrangian, we shall use LinearConstraints to constrain the problem.
double[,] a = Matrix.Identity(2); // Set up the constraint matrix...
double[] b = Vector.Zeros(2); // ...and the values they must be greater than
int numberOfEqualities = 0;
var linearConstraints = LinearConstraintCollection.Create(a, b, numberOfEqualities);
// Finally, we create the non-linear programming solver
var solver = new AugmentedLagrangian(f, linearConstraints);
// And attempt to find a minimum
bool success = solver.Minimize();
// The solution found was { 1, 1 }
double[] solution = solver.Solution;
// with the minimum value zero.
double minValue = solver.Value;
#endregion
Assert.IsTrue(success);
Assert.AreEqual(0, minValue, 1e-10);
Assert.AreEqual(1, solver.Solution[0], 1e-6);
Assert.AreEqual(1, solver.Solution[1], 1e-6);
Assert.IsFalse(double.IsNaN(minValue));
Assert.IsFalse(double.IsNaN(solver.Solution[0]));
Assert.IsFalse(double.IsNaN(solver.Solution[1]));
}
public void ConstructorTest2()
{
// https://github.com/accord-net/framework/issues/171
int n = 21;
var Q = Matrix.Diagonal(n, 2.0);
var d = Vector.Create(3132.0, 6264, 15660, 18792, 21924, 6264, 18792, 21924, 9396, 3132, 12528, 6264, 9396, 18792, 21924, 9396, 3132, 3132, 6264, 15660, 18792);
int m = 44;
double[] b =
{
703.999,
-704.001,
1267.999,
-1268.001,
1565.999,
-1566.001,
471.999,
-472.001,
1425.999,
-1426.001,
-107.001,
-1164.001,
-57.001,
-311.001,
-1433.001,
-0.001,
-0.001,
-788.001,
-472.001,
-850.001,
-273.001,
-0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001
};
var A = Matrix.Create(m, n,
1.0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1,
0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0,
0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0,
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0,
0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0,
0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0,
0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0,
0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
var aa = A.Reshape();
var qq = Q.Reshape();
var r = Quadprog.Compute(n, m, aa, b, 0, qq, d);
double[] expected = r.Item2;
var constraints = LinearConstraintCollection.Create(A, b, 0);
double[] expectedViolation = constraints.Apply(x => x.GetViolation(r.Item2));
for (int i = 0; i < expectedViolation.Length; i++)
{
Assert.IsTrue(expectedViolation[i] >= -1e-11);
}
var solver = new GoldfarbIdnani(Q, d.Multiply(-1), A, b, 0);
Assert.IsTrue(solver.Minimize());
double[] actual = solver.Solution;
Assert.IsTrue(actual.IsEqual(expected, 1e-3));
double[] actualViolation = constraints.Apply(x => x.GetViolation(solver.Solution));
Assert.IsTrue(actualViolation.IsEqual(expectedViolation, 1e-3));
}