public static double solve (bool isFine, IEnumerable<Constraint> cons)
{
var constraints = cons.ToArray ();
// Get the parameters that need solving by selecting "free" ones
Parameter[] x = constraints.SelectMany (p=>p)
.Distinct ()
.Where(p=>p.free==true)
.ToArray ();
Console.WriteLine ("Number of free vars is " + x.Length);
// Wrap our constraint error function for Accord.NET
Func<double[], double> objective = args => {
int i = 0;
foreach (var arg in args) {
x [i].Value = arg;
i++;
}
return Constraint.calc (constraints);
};
var nlConstraints = new List<NonlinearConstraint> ();
// Finally, we create the non-linear programming solver
var solver = new AugmentedLagrangianSolver(x.Length, nlConstraints);
// Copy in the initial conditions
x.Select(v=>v.Value).ToArray().CopyTo (solver.Solution,0);
// And attempt to solve the problem
return solver.Minimize(LogWrap(objective), LogWrap(Grad(x.Length, objective)));
}
public void AugmentedLagrangianSolverConstructorTest1()
{
// min 100(y-x*x)²+(1-x)²
//
// s.t. x <= 0
// y <= 0
//
var f = new NonlinearObjectiveFunction(2,
function: (x) => 100 * Math.Pow(x[1] - x[0] * x[0], 2) + Math.Pow(1 - x[0], 2),
gradient: (x) => new[]
{
2.0 * (200.0 * x[0]*x[0]*x[0] - 200.0 * x[0] * x[1] + x[0] - 1), // df/dx
200 * (x[1] - x[0]*x[0]) // df/dy
}
);
var constraints = new List<NonlinearConstraint>();
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[0],
gradient: (x) => new[] { 1.0, 0.0 },
shouldBe: ConstraintType.LesserThanOrEqualTo, value: 0
));
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[1],
gradient: (x) => new[] { 0.0, 1.0 },
shouldBe: ConstraintType.LesserThanOrEqualTo, value: 0
));
var solver = new AugmentedLagrangianSolver(2, constraints);
double minValue = solver.Minimize(f);
Assert.AreEqual(1, minValue, 1e-5);
Assert.AreEqual(0, solver.Solution[0], 1e-5);
Assert.AreEqual(0, solver.Solution[1], 1e-5);
}
public void AugmentedLagrangianSolverConstructorTest7()
{
// maximize 2x + 3y, s.t. 2x² + 2y² <= 50
// Max x' * c
// x
// s.t. x' * A * x <= k
// x' * i = 1
// lower_bound < x < upper_bound
double[] c = { 2, 3 };
double[,] A = { { 2, 0 }, { 0, 2 } };
double k = 50;
// Create the objective function
var objective = new NonlinearObjectiveFunction(2,
function: (x) => x.InnerProduct(c),
gradient: (x) => c
);
// Test objective
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
double expected = i * 2 + j * 3;
double actual = objective.Function(new double[] { i, j });
Assert.AreEqual(expected, actual);
}
}
// Create the optimization constraints
var constraints = new List<NonlinearConstraint>();
constraints.Add(new QuadraticConstraint(objective,
quadraticTerms: A,
shouldBe: ConstraintType.LesserThanOrEqualTo, value: k
));
// Test first constraint
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
double expected = i * (2 * i + 0 * j) + j * (0 * i + 2 * j);
double actual = constraints[0].Function(new double[] { i, j });
Assert.AreEqual(expected, actual);
}
}
// Create the solver algorithm
AugmentedLagrangianSolver solver =
new AugmentedLagrangianSolver(2, constraints);
double maxValue = solver.Maximize(objective);
Assert.AreEqual(18.02, maxValue, 0.01);
Assert.AreEqual(2.77, solver.Solution[0], 1e-2);
Assert.AreEqual(4.16, solver.Solution[1], 1e-2);
}
public void AugmentedLagrangianSolverConstructorTest5()
{
// 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)
//
double x = 0, y = 0;
// First, we create our objective function
var f = new NonlinearObjectiveFunction(
// This is the objective function: f(x,y) = min 100(y-x²)²+(1-x)²
function: () => 100 * Math.Pow(y - x * x, 2) + Math.Pow(1 - x, 2),
// The gradient vector:
gradient: () => new[]
{
2 * (200 * Math.Pow(x, 3) - 200 * x * y + x - 1), // df/dx = 2(200x³-200xy+x-1)
200 * (y - x*x) // df/dy = 200(y-x²)
}
);
// Now we can start stating the constraints
var constraints = new List<NonlinearConstraint>();
// Add the non-negativity constraint for x
constraints.Add(new NonlinearConstraint(f,
// 1st contraint: x should be greater than or equal to 0
function: () => x, shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0,
gradient: () => new[] { 1.0, 0.0 }
));
// Add the non-negativity constraint for y
constraints.Add(new NonlinearConstraint(f,
// 2nd constraint: y should be greater than or equal to 0
function: () => y, shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0,
gradient: () => new[] { 0.0, 1.0 }
));
// Finally, we create the non-linear programming solver
var solver = new AugmentedLagrangianSolver(2, constraints);
// And attempt to solve the problem
double minValue = solver.Minimize(f);
Assert.AreEqual(0, minValue, 1e-10);
Assert.AreEqual(1, solver.Solution[0], 1e-10);
Assert.AreEqual(1, solver.Solution[1], 1e-10);
Assert.IsFalse(Double.IsNaN(minValue));
Assert.IsFalse(Double.IsNaN(solver.Solution[0]));
Assert.IsFalse(Double.IsNaN(solver.Solution[1]));
}
public void AugmentedLagrangianSolverConstructorTest4()
{
// min x*y+ y*z
//
// s.t. x^2 - y^2 + z^2 - 2 >= 0
// x^2 + y^2 + z^2 - 10 <= 0
// x + y = 1
//
double x = 0, y = 0, z = 0;
var f = new NonlinearObjectiveFunction(
function: () => x * y + y * z,
gradient: () => new[]
{
y, // df/dx
x + z, // df/dy
y, // df/dz
}
);
var constraints = new List<NonlinearConstraint>();
constraints.Add(new NonlinearConstraint(f,
function: () => x * x - y * y + z * z,
gradient: () => new[] { 2 * x, -2 * y, 2 * z },
shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 2
));
constraints.Add(new NonlinearConstraint(f,
function: () => x * x + y * y + z * z,
gradient: () => new[] { 2 * x, 2 * y, 2 * z },
shouldBe: ConstraintType.LesserThanOrEqualTo, value: 10
));
constraints.Add(new NonlinearConstraint(f,
function: () => x + y,
gradient: () => new[] { 1.0, 1.0, 0.0 },
shouldBe: ConstraintType.EqualTo, value: 1
)
{
Tolerance = 1e-5
});
var solver = new AugmentedLagrangianSolver(3, constraints);
solver.Solution[0] = 1;
solver.Solution[1] = 1;
solver.Solution[2] = 1;
double minValue = solver.Minimize(f);
Assert.AreEqual(1, solver.Solution[0] + solver.Solution[1], 1e-5);
Assert.IsFalse(Double.IsNaN(minValue));
Assert.IsFalse(Double.IsNaN(solver.Solution[0]));
Assert.IsFalse(Double.IsNaN(solver.Solution[1]));
Assert.IsFalse(Double.IsNaN(solver.Solution[2]));
}
public void AugmentedLagrangianSolverConstructorTest6()
{
// Max x' * c
// x
// s.t. x' * A * x <= k
// x' * i = 1
// lower_bound < x < upper_bound
double[] c = { 2, 3 };
double[,] A = { { 2, 0 }, { 0, 2 } };
double k = 50;
// Create the objective function
var objective = new NonlinearObjectiveFunction(2,
function: (x) => x.InnerProduct(c),
gradient: (x) => c
);
// Test objective
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
double expected = i * 2 + j * 3;
double actual = objective.Function(new double[] { i, j });
Assert.AreEqual(expected, actual);
}
}
// Create the optimization constraints
var constraints = new List<NonlinearConstraint>();
constraints.Add(new QuadraticConstraint(objective,
quadraticTerms: A,
shouldBe: ConstraintType.LesserThanOrEqualTo, value: k
));
constraints.Add(new NonlinearConstraint(objective,
function: (x) => x.Sum(),
gradient: (x) => new[] { 1.0, 1.0 },
shouldBe: ConstraintType.EqualTo, value: 1,
withinTolerance: 1e-3
));
// Test first constraint
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
double expected = i * (2 * i + 0 * j) + j * (0 * i + 2 * j);
double actual = constraints[0].Function(new double[] { i, j });
Assert.AreEqual(expected, actual);
}
}
// Test second constraint
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
double expected = i + j;
double actual = constraints[1].Function(new double[] { i, j });
Assert.AreEqual(expected, actual);
}
}
// Create the solver algorithm
AugmentedLagrangianSolver solver =
new AugmentedLagrangianSolver(2, constraints);
double minValue = solver.Maximize(objective);
Assert.AreEqual(7.42443, minValue, 1e-5);
Assert.AreEqual(-4.42433, solver.Solution[0], 1e-5);
Assert.AreEqual(5.42433, solver.Solution[1], 1e-5);
}
