/// <summary>
/// Minimizes the function.
/// </summary>
///
/// <param name="function">The function to be minimized.</param>
/// <returns>The minimum value at the solution found.</returns>
///
public double Minimize(QuadraticObjectiveFunction function)
{
if (function == null)
{
throw new ArgumentNullException("function");
}
return(Minimize(function.GetQuadraticTermsMatrix(), function.GetLinearTermsVector()));
}
/// <summary>
/// Minimizes the function.
/// </summary>
///
/// <param name="function">The function to be minimized.</param>
/// <returns>The minimum value at the solution found.</returns>
///
public double Minimize(QuadraticObjectiveFunction function)
{
if (function == null)
throw new ArgumentNullException("function");
double[,] Q = function.GetQuadraticTermsMatrix();
double[] d = function.GetLinearTermsVector();
return Minimize(Q, d);
}
/// <summary>
/// Minimizes the function.
/// </summary>
///
/// <param name="function">The function to be minimized.</param>
/// <returns>The minimum value at the solution found.</returns>
///
public double Minimize(QuadraticObjectiveFunction function)
{
if (function == null)
throw new ArgumentNullException("function");
double[,] Q = function.GetQuadraticTermsMatrix();
double[] d = function.GetLinearTermsVector();
return Minimize(Q, d);
}
public void GoldfarbIdnaniConstructorTest9()
{
// Solve the following optimization problem:
//
// min f(x) = 2x² + xy + y² - 5y
//
// s.t. -x - 3y >= -2
// -x - y >= 0
// x >= 0
// y >= 0
//
double x = 0, y = 0;
var f = new QuadraticObjectiveFunction(() => 2 * (x * x) + (x * y) + (y * y) - 5 * y);
List<LinearConstraint> constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, () => -x - 3 * y >= -2));
constraints.Add(new LinearConstraint(f, () => -x - y >= 0));
constraints.Add(new LinearConstraint(f, () => x >= 0));
constraints.Add(new LinearConstraint(f, () => y >= 0));
GoldfarbIdnaniQuadraticSolver target = new GoldfarbIdnaniQuadraticSolver(2, constraints);
double[,] expectedA =
{
{ -1, -3 },
{ -1, -1 },
{ 1, 0 },
{ 0, 1 },
};
double[] expectedb =
{
-2, 0, 0, 0
};
double[,] expectedQ =
{
{ 4, 1 },
{ 1, 2 },
};
double[] expectedd =
{
0, -5
};
// Tested against R's QuadProg package
/*
Qmat = matrix(c(4,1,1,2),2,2)
dvec = -c(0, -5)
Amat = matrix(c(-1, -3, -1, -1, 1, 0, 0, 1), 2,4)
bvec = c(-2, 0, 0, 0)
solve.QP(Qmat, dvec, Amat, bvec)
*/
var actualA = target.ConstraintMatrix;
var actualb = target.ConstraintValues;
var actualQ = f.GetQuadraticTermsMatrix();
var actuald = f.GetLinearTermsVector();
Assert.IsTrue(expectedA.IsEqual(actualA));
Assert.IsTrue(expectedb.IsEqual(actualb));
Assert.IsTrue(expectedQ.IsEqual(actualQ));
Assert.IsTrue(expectedd.IsEqual(actuald));
double min = target.Minimize(f);
double[] solution = target.Solution;
Assert.AreEqual(0, solution[0], 1e-10);
Assert.AreEqual(0, solution[1], 1e-10);
Assert.AreEqual(0.0, min, 1e-10);
Assert.AreEqual(0, target.Lagrangian[0], 1e-10);
Assert.AreEqual(5, target.Lagrangian[1], 1e-10);
Assert.AreEqual(5, target.Lagrangian[2], 1e-10);
Assert.AreEqual(0, target.Lagrangian[3], 1e-10);
Assert.IsFalse(Double.IsNaN(min));
foreach (double v in target.Solution)
Assert.IsFalse(double.IsNaN(v));
foreach (double v in target.Lagrangian)
Assert.IsFalse(double.IsNaN(v));
}
public void GoldfarbIdnaniConstructorTest8()
{
// Solve the following optimization problem:
//
// min f(x) = x² + 2xy + y² - y
//
// s.t. x >= 1
// y >= 1
//
double x = 0, y = 0;
// http://www.wolframalpha.com/input/?i=min+x%C2%B2+%2B+2xy+%2B+y%C2%B2+-+y%2C+x+%3E%3D+1%2C+y+%3E%3D+1
var f = new QuadraticObjectiveFunction(() => (x * x) + 2 * (x * y) + (y * y) - y);
List<LinearConstraint> constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, () => x >= 1));
constraints.Add(new LinearConstraint(f, () => y >= 1));
GoldfarbIdnaniQuadraticSolver target = new GoldfarbIdnaniQuadraticSolver(2, constraints);
double[,] A =
{
{ 1, 0 },
{ 0, 1 },
};
double[] b =
{
1,
1,
};
Assert.IsTrue(A.IsEqual(target.ConstraintMatrix));
Assert.IsTrue(b.IsEqual(target.ConstraintValues));
double[,] Q =
{
{ 2, 2 },
{ 2, 2 },
};
double[] d = { 0, -1 };
var actualQ = f.GetQuadraticTermsMatrix();
var actuald = f.GetLinearTermsVector();
Assert.IsTrue(Q.IsEqual(actualQ));
Assert.IsTrue(d.IsEqual(actuald));
bool thrown = false;
try
{
target.Minimize(f);
}
catch (NonPositiveDefiniteMatrixException)
{
thrown = true;
}
Assert.IsTrue(thrown);
}
public void GoldfarbIdnaniConstructorTest7()
{
// Solve the following optimization problem:
//
// min f(x) = 3x² + 2xy + 3y² - y
//
// s.t. x >= 1
// y >= 1
//
double x = 0, y = 0;
// http://www.wolframalpha.com/input/?i=min+x%C2%B2+%2B+2xy+%2B+y%C2%B2+-+y%2C+x+%3E%3D+1%2C+y+%3E%3D+1
var f = new QuadraticObjectiveFunction(() => 3 * (x * x) + 2 * (x * y) + 3 * (y * y) - y);
List<LinearConstraint> constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, () => x >= 1));
constraints.Add(new LinearConstraint(f, () => y >= 1));
GoldfarbIdnaniQuadraticSolver target = new GoldfarbIdnaniQuadraticSolver(2, constraints);
double[,] A =
{
{ 1, 0 },
{ 0, 1 },
};
double[] b =
{
1,
1,
};
Assert.IsTrue(A.IsEqual(target.ConstraintMatrix));
Assert.IsTrue(b.IsEqual(target.ConstraintValues));
double[,] Q =
{
{ 6, 2 },
{ 2, 6 },
};
double[] d = { 0, -1 };
var actualQ = f.GetQuadraticTermsMatrix();
var actuald = f.GetLinearTermsVector();
Assert.IsTrue(Q.IsEqual(actualQ));
Assert.IsTrue(d.IsEqual(actuald));
double minValue = target.Minimize(f);
double[] solution = target.Solution;
Assert.AreEqual(7, minValue);
Assert.AreEqual(1, solution[0]);
Assert.AreEqual(1, solution[1]);
Assert.AreEqual(8, target.Lagrangian[0], 1e-5);
Assert.AreEqual(7, target.Lagrangian[1], 1e-5);
foreach (double v in target.Solution)
Assert.IsFalse(double.IsNaN(v));
foreach (double v in target.Lagrangian)
Assert.IsFalse(double.IsNaN(v));
}
public void GoldfarbIdnaniConstructorTest4()
{
// Solve the following optimization problem:
//
// min f(x) = 2x² - xy + 4y² - 5x - 6y
//
// s.t. x - y == 5 (x minus y should be equal to 5)
// x >= 10 (x should be greater than or equal to 10)
//
var f = new QuadraticObjectiveFunction("2x² - xy + 4y² - 5x - 6y");
List<LinearConstraint> constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, "x-y = 5"));
constraints.Add(new LinearConstraint(f, "x >= 10"));
GoldfarbIdnaniQuadraticSolver target = new GoldfarbIdnaniQuadraticSolver(2, constraints);
double[,] A =
{
{ 1, -1 },
{ 1, 0 },
};
double[] b =
{
5,
10,
};
Assert.IsTrue(A.IsEqual(target.ConstraintMatrix));
Assert.IsTrue(b.IsEqual(target.ConstraintValues));
double[,] Q =
{
{ +2*2, -1 },
{ -1, +4*2 },
};
double[] d = { -5, -6 };
var actualQ = f.GetQuadraticTermsMatrix();
var actuald = f.GetLinearTermsVector();
Assert.IsTrue(Q.IsEqual(actualQ));
Assert.IsTrue(d.IsEqual(actuald));
}
public void GoldfarbIdnaniConstructorTest3()
{
// Solve the following optimization problem:
//
// min f(x) = 2x² - xy + 4y² - 5x - 6y
//
// s.t. x - y == 5 (x minus y should be equal to 5)
// x >= 10 (x should be greater than or equal to 10)
//
// In this example we will be using some symbolic processing.
// The following variables could be initialized to any value.
double x = 0, y = 0;
// Create our objective function using a lambda expression
var f = new QuadraticObjectiveFunction(() => 2 * (x * x) - (x * y) + 4 * (y * y) - 5 * x - 6 * y);
// Now, create the constraints
List<LinearConstraint> constraints = new List<LinearConstraint>();
constraints.Add(new LinearConstraint(f, () => x - y == 5));
constraints.Add(new LinearConstraint(f, () => x >= 10));
// Now we create the quadratic programming solver for 2 variables, using the constraints.
GoldfarbIdnaniQuadraticSolver solver = new GoldfarbIdnaniQuadraticSolver(2, constraints);
double[,] A =
{
{ 1, -1 },
{ 1, 0 },
};
double[] b =
{
5,
10,
};
Assert.IsTrue(A.IsEqual(solver.ConstraintMatrix));
Assert.IsTrue(b.IsEqual(solver.ConstraintValues));
double[,] Q =
{
{ +2*2, -1 },
{ -1, +4*2 },
};
double[] d = { -5, -6 };
var actualQ = f.GetQuadraticTermsMatrix();
var actuald = f.GetLinearTermsVector();
Assert.IsTrue(Q.IsEqual(actualQ));
Assert.IsTrue(d.IsEqual(actuald));
// And attempt to solve it.
double minimumValue = solver.Minimize(f);
}
/// <summary>
/// Maximizes the function.
/// </summary>
///
/// <param name="function">The function to be maximized.</param>
/// <returns>The maximum value at the solution found.</returns>
///
public double Maximize(QuadraticObjectiveFunction function)
{
if (function == null)
throw new ArgumentNullException("function");
return Maximize(function.GetQuadraticTermsMatrix(), function.GetLinearTermsVector());
}
