/// <summary>
/// Maximizes the given function.
/// </summary>
///
/// <param name="function">The function to be maximized.</param>
///
/// <returns>The maximum value found at the <see cref="Solution"/>.</returns>
///
public double Maximize(NonlinearObjectiveFunction function)
{
if (function.NumberOfVariables != numberOfVariables)
{
throw new ArgumentOutOfRangeException("function",
"Incorrect number of variables in the objective function. " +
"The number of variables must match the number of variables set in the solver.");
}
this.Function = x => - function.Function(x);
this.Gradient = x => function.Gradient(x).Multiply(-1);
minimize();
return(-Function(Solution));
}
public void ConstructorTest4()
{
var function = new NonlinearObjectiveFunction(2, x =>
Math.Pow(x[0] * x[0] - x[1], 2.0) + Math.Pow(1.0 + x[0], 2.0));
NelderMead solver = new NelderMead(function);
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
Assert.AreEqual(0, minimum, 1e-10);
Assert.AreEqual(-1, solution[0], 1e-5);
Assert.AreEqual(1, solution[1], 1e-4);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest5()
{
var function = new NonlinearObjectiveFunction(2, x =>
10.0 * Math.Pow(x[0] * x[0] - x[1], 2.0) + Math.Pow(1.0 + x[0], 2.0));
Subplex solver = new Subplex(function);
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
Assert.AreEqual(-0, minimum, 1e-6);
Assert.AreEqual(-1, solution[0], 1e-3);
Assert.AreEqual(+1, solution[1], 1e-3);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest3()
{
// minimize f(x) = x*y*z,
// s.t.
//
// 1 - x² - 2y² - 3z² > 0
// x > 0,
// y > 0
//
// Easy three dimensional minimization in ellipsoid.
var function = new NonlinearObjectiveFunction(3,
function: x => x[0] * x[1] * x[2],
gradient: x => new[] { x[1] * x[2], x[0] * x[2], x[0] * x[1] });
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(3,
function: x => 1.0 - x[0] * x[0] - 2.0 * x[1] * x[1] - 3.0 * x[2] * x[2],
gradient: x => new[] { -2.0 * x[0], -4.0 * x[1], -6.0 * x[2] }),
new NonlinearConstraint(3,
function: x => x[0],
gradient: x => new[] { 1.0, 0, 0 }),
new NonlinearConstraint(3,
function: x => x[1],
gradient: x => new[] { 0, 1.0, 0 }),
new NonlinearConstraint(3,
function: x => -x[2],
gradient: x => new[] { 0, 0, -1.0 }),
};
for (int i = 0; i < constraints.Length; i++)
{
Assert.AreEqual(ConstraintType.GreaterThanOrEqualTo, constraints[i].ShouldBe);
Assert.AreEqual(0, constraints[i].Value);
}
var inner = new BroydenFletcherGoldfarbShanno(3);
inner.LineSearch = LineSearch.BacktrackingArmijo;
inner.Corrections = 10;
var solver = new AugmentedLagrangian(inner, function, constraints);
Assert.AreEqual(inner, solver.Optimizer);
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
double[] expected =
{
1.0 / Math.Sqrt(3.0), 1.0 / Math.Sqrt(6.0), -1.0 / 3.0
};
for (int i = 0; i < expected.Length; i++)
Assert.AreEqual(expected[i], solver.Solution[i], 1e-3);
Assert.AreEqual(-0.078567420132031968, minimum, 1e-4);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest4()
{
// Weak version of Rosenbrock's problem.
var function = new NonlinearObjectiveFunction(2, x =>
Math.Pow(x[0] * x[0] - x[1], 2.0) + Math.Pow(1.0 + x[0], 2.0));
Subplex solver = new Subplex(function);
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
Assert.AreEqual(2, solution.Length);
Assert.AreEqual(0, minimum, 1e-10);
Assert.AreEqual(-1, solution[0], 1e-5);
Assert.AreEqual(1, solution[1], 1e-4);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
private static void test2(IGradientOptimizationMethod inner)
{
// maximize 2x + 3y, s.t. 2x² + 2y² <= 50
//
// http://www.wolframalpha.com/input/?i=max+2x+%2B+3y%2C+s.t.+2x%C2%B2+%2B+2y%C2%B2+%3C%3D+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++)
{
var input = new double[] { i, j };
double expected = i * (2 * i + 0 * j) + j * (0 * i + 2 * j);
double actual = constraints[0].Function(input);
Assert.AreEqual(expected, actual);
}
}
// Create the solver algorithm
AugmentedLagrangian solver =
new AugmentedLagrangian(inner, objective, constraints);
Assert.AreEqual(inner, solver.Optimizer);
Assert.IsTrue(solver.Maximize());
double maxValue = solver.Value;
Assert.AreEqual(18.02, maxValue, 1e-2);
Assert.AreEqual(2.77, solver.Solution[0], 1e-2);
Assert.AreEqual(4.16, solver.Solution[1], 1e-2);
}
public void ConstructorTest2()
{
Accord.Math.Tools.SetupGenerator(0);
var function = new NonlinearObjectiveFunction(2,
function: x => x[0] * x[1],
gradient: x => new[] { x[1], x[0] });
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(function,
function: x => 1.0 - x[0] * x[0] - x[1] * x[1],
gradient: x => new [] { -2 * x[0], -2 * x[1]}),
new NonlinearConstraint(function,
function: x => x[0],
gradient: x => new [] { 1.0, 0.0}),
};
var target = new ConjugateGradient(2);
AugmentedLagrangian solver = new AugmentedLagrangian(target, function, constraints);
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
double sqrthalf = Math.Sqrt(0.5);
Assert.AreEqual(-0.5, minimum, 1e-5);
Assert.AreEqual(sqrthalf, solution[0], 1e-5);
Assert.AreEqual(-sqrthalf, solution[1], 1e-5);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest6_2()
{
/// This problem is taken from Fletcher's book Practical Methods of
/// Optimization and has the equation number (9.1.15).
var function = new NonlinearObjectiveFunction(2, x => -x[0] - x[1]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(2, x => -(x[1] - x[0] * x[0]) <= 0),
new NonlinearConstraint(2, x => -(-x[0] * x[0] - x[1] * x[1]) <= 1.0),
};
Cobyla cobyla = new Cobyla(function, constraints);
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
double sqrthalf = Math.Sqrt(0.5);
Assert.AreEqual(-sqrthalf * 2, minimum, 1e-10);
Assert.AreEqual(sqrthalf, solution[0], 1e-5);
Assert.AreEqual(sqrthalf, solution[1], 1e-5);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
private static void test1(IGradientOptimizationMethod inner, double tol)
{
// maximize 2x + 3y, s.t. 2x² + 2y² <= 50 and x+y = 1
// 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-10
));
// 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);
}
}
AugmentedLagrangian solver =
new AugmentedLagrangian(inner, objective, constraints);
Assert.AreEqual(inner, solver.Optimizer);
Assert.IsTrue(solver.Maximize());
double maxValue = solver.Value;
Assert.AreEqual(6, maxValue, tol);
Assert.AreEqual(-3, solver.Solution[0], tol);
Assert.AreEqual(4, solver.Solution[1], tol);
}
public void SubspaceTest1()
{
var function = new NonlinearObjectiveFunction(5, x =>
10.0 * Math.Pow(x[0] * x[0] - x[1], 2.0) + Math.Pow(1.0 + x[0], 2.0));
NelderMead solver = new NelderMead(function);
solver.NumberOfVariables = 2;
Assert.IsTrue(solver.Minimize());
double minimum = solver.Value;
double[] solution = solver.Solution;
Assert.AreEqual(5, solution.Length);
Assert.AreEqual(-0, minimum, 1e-6);
Assert.AreEqual(-1, solution[0], 1e-3);
Assert.AreEqual(+1, solution[1], 1e-3);
double expectedMinimum = function.Function(solver.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest3()
{
// Easy three dimensional minimization in ellipsoid.
var function = new NonlinearObjectiveFunction(3, x => x[0] * x[1] * x[2]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(3, x => 1.0 - x[0] * x[0] - 2.0 * x[1] * x[1] - 3.0 * x[2] * x[2])
};
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 sqrthalf = Math.Sqrt(0.5);
double[] expected =
{
1.0 / Math.Sqrt(3.0), 1.0 / Math.Sqrt(6.0), -1.0 / 3.0
};
for (int i = 0; i < expected.Length; i++)
Assert.AreEqual(expected[i], cobyla.Solution[i], 1e-4);
Assert.AreEqual(-0.078567420132031968, minimum, 1e-10);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
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);
}
public void ConstructorTest2()
{
var function = new NonlinearObjectiveFunction(2, x => x[0] * x[1]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(function, x => 1.0 - x[0] * x[0] - x[1] * x[1])
};
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 sqrthalf = Math.Sqrt(0.5);
Assert.AreEqual(-0.5, minimum, 1e-10);
Assert.AreEqual(sqrthalf, solution[0], 1e-5);
Assert.AreEqual(-sqrthalf, solution[1], 1e-5);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest9()
{
/// This problem is taken from page 111 of Hock and Schittkowski's
/// book Test Examples for Nonlinear Programming Codes. It is their
/// test problem Number 100.
///
var function = new NonlinearObjectiveFunction(7, x =>
Math.Pow(x[0] - 10.0, 2.0) + 5.0 * Math.Pow(x[1] - 12.0, 2.0) + Math.Pow(x[2], 4.0) +
3.0 * Math.Pow(x[3] - 11.0, 2.0) + 10.0 * Math.Pow(x[4], 6.0) + 7.0 * x[5] * x[5] + Math.Pow(x[6], 4.0) -
4.0 * x[5] * x[6] - 10.0 * x[5] - 8.0 * x[6]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(7, x => 127.0 - 2.0 * x[0] * x[0] - 3.0 * Math.Pow(x[1], 4.0)
- x[2] - 4.0 * x[3] * x[3] - 5.0 * x[4]),
new NonlinearConstraint(7, x => 282.0 - 7.0 * x[0] - 3.0 * x[1] - 10.0 * x[2] * x[2] - x[3] + x[4]),
new NonlinearConstraint(7, x => 196.0 - 23.0 * x[0] - x[1] * x[1] - 6.0 * x[5] * x[5] + 8.0 * x[6]),
new NonlinearConstraint(7, x => -4.0 * x[0] * x[0] - x[1] * x[1] + 3.0 * x[0] * x[1]
- 2.0 * x[2] * x[2] - 5.0 * x[5] + 11.0 * x[6])
};
Cobyla cobyla = new Cobyla(function, constraints);
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
double[] expected =
{
2.330499, 1.951372, -0.4775414, 4.365726, -0.624487, 1.038131, 1.594227
};
for (int i = 0; i < expected.Length; i++)
Assert.AreEqual(expected[i], cobyla.Solution[i], 1e-4);
Assert.AreEqual(680.63005737443393, minimum, 1e-6);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest8()
{
/// This problem is taken from page 66 of Hock and Schittkowski's book Test
/// Examples for Nonlinear Programming Codes. It is their test problem Number
/// 43, and has the name Rosen-Suzuki.
var function = new NonlinearObjectiveFunction(4, x => x[0] * x[0]
+ x[1] * x[1] + 2.0 * x[2] * x[2]
+ x[3] * x[3] - 5.0 * x[0] - 5.0 * x[1]
- 21.0 * x[2] + 7.0 * x[3]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(4, x=> 8.0 - x[0] * x[0]
- x[1] * x[1] - x[2] * x[2] - x[3] * x[3] - x[0] + x[1] - x[2] + x[3]),
new NonlinearConstraint(4, x => 10.0 - x[0] * x[0]
- 2.0 * x[1] * x[1] - x[2] * x[2] - 2.0 * x[3] * x[3] + x[0] + x[3]),
new NonlinearConstraint(4, x => 5.0 - 2.0 * x[0] * x[0]
- x[1] * x[1] - x[2] * x[2] - 2.0 * x[0] + x[1] + x[3])
};
Cobyla cobyla = new Cobyla(function, constraints);
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
double[] expected =
{
0.0, 1.0, 2.0, -1.0
};
for (int i = 0; i < expected.Length; i++)
Assert.AreEqual(expected[i], cobyla.Solution[i], 1e-4);
Assert.AreEqual(-44, minimum, 1e-10);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
public void ConstructorTest7()
{
/// This problem is taken from Fletcher's book Practical Methods of
/// Optimization and has the equation number (14.4.2).
var function = new NonlinearObjectiveFunction(3, x => x[2]);
NonlinearConstraint[] constraints =
{
new NonlinearConstraint(3, x=> 5.0 * x[0] - x[1] + x[2]),
new NonlinearConstraint(3, x => x[2] - x[0] * x[0] - x[1] * x[1] - 4.0 * x[1]),
new NonlinearConstraint(3, x => x[2] - 5.0 * x[0] - x[1]),
};
Cobyla cobyla = new Cobyla(function, constraints);
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
Assert.AreEqual(-3, minimum, 1e-5);
Assert.AreEqual(0.0, solution[0], 1e-5);
Assert.AreEqual(-3.0, solution[1], 1e-5);
Assert.AreEqual(-3.0, solution[2], 1e-5);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
/// <summary>
/// Maximizes the given function.
/// </summary>
///
/// <param name="function">The function to be maximized.</param>
///
/// <returns>The maximum value found at the <see cref="Solution"/>.</returns>
///
public double Maximize(NonlinearObjectiveFunction function)
{
if (function.NumberOfVariables != numberOfVariables)
throw new ArgumentOutOfRangeException("function",
"Incorrect number of variables in the objective function. " +
"The number of variables must match the number of variables set in the solver.");
this.Function = x => -function.Function(x);
this.Gradient = x => function.Gradient(x).Multiply(-1);
minimize();
return -Function(Solution);
}
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 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);
}
public void ConstructorTest5()
{
// Intermediate version of Rosenbrock's problem.
var function = new NonlinearObjectiveFunction(2, x =>
10.0 * Math.Pow(x[0] * x[0] - x[1], 2.0) + Math.Pow(1.0 + x[0], 2.0));
Cobyla cobyla = new Cobyla(function);
Assert.IsTrue(cobyla.Minimize());
double minimum = cobyla.Value;
double[] solution = cobyla.Solution;
Assert.AreEqual(-0, minimum, 1e-6);
Assert.AreEqual(-1, solution[0], 1e-3);
Assert.AreEqual(+1, solution[1], 1e-3);
double expectedMinimum = function.Function(cobyla.Solution);
Assert.AreEqual(expectedMinimum, minimum);
}
