public void FindMinimum_TestFunction1WithConstraints_AnalyticResult()
{
/* Constraints:
* x_0 + x_1 = 3,
* x_0 >= 0,
* x_1 >= 0,
* x_0 + x_2 >= 2 */
var optimizer = new GoldfarbIdanaQuadraticProgram();
var boxConstraint = optimizer.Constraint.Create(MultiDimRegion.Interval.Create(2, new[] { 0.0, 0.0 }, new[] { Double.NaN, Double.NaN }));
var equalityConstraint = optimizer.Constraint.Create(new MultiDimRegion.LinearEquality(new DenseMatrix(2, 1, new[] { 1.0, 1.0 }), new[] { 3.0 }));
var inequalityConstraint = optimizer.Constraint.Create(new MultiDimRegion.LinearInequality(new DenseMatrix(2, 1, new[] { 1.0, 1.0 }), new[] { 2.0 }));
var algorithm = optimizer.Create(boxConstraint, equalityConstraint, inequalityConstraint);
var A = new DenseMatrix(2, 2, new[] { 4.0, -2.0, -2.0, 4 - 0 }); // = (4 & -2 \\ -2 & 4)
var b = new[] { 6.0, 0.0 };
algorithm.Function = optimizer.Function.Create(A, b);
var actualArgMin = new double[2];
double actualMinimum;
var state = algorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedArgMin = new[] { 1.0, 2.0 };
var expectedMinimum = 12.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
Assert.That(actualArgMin, Is.EqualTo(expectedArgMin).AsCollection.Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
}
public void FindMinimum_TestFunction3WithConstraints_AnalyticResult()
{
/* minimize:
* f(x) = - 8 * x_0 - 16 * x_1 + x_0^2 + 4 * x_1^2
*
* subject to x_0 + x_1 <= 5, x_0 <? 3, x_0 >= 0, x_1 >= 0 */
var optimizer = new GoldfarbIdanaQuadraticProgram();
var boxConstraint = optimizer.Constraint.Create(MultiDimRegion.Interval.Create(2, new[] { 0.0, 0.0 }, new[] { 3.0, Double.NaN }));
var inequalityConstraint = optimizer.Constraint.Create(new MultiDimRegion.LinearInequality(new DenseMatrix(2, 1, new[] { -1.0, -1.0 }), new[] { -5.0 }));
var algorithm = optimizer.Create(boxConstraint, inequalityConstraint);
var A = new DenseMatrix(2, 2, new[] { 2.0, 0.0, 0.0, 8.0 });
var b = new[] { -8.0, -16.0 };
algorithm.Function = optimizer.Function.Create(A, b);
var actualArgMin = new double[2];
double actualMinimum;
var state = algorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedArgMin = new[] { 3.0, 2.0 };
var expectedMinimum = -31.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
Assert.That(actualArgMin, Is.EqualTo(expectedArgMin).AsCollection.Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
}
public void FindMinimum_TestFunction1NoConstraints_AnalyticResult()
{
var optimizer = new GoldfarbIdanaQuadraticProgram();
var algorithm = optimizer.Create(2);
var A = new DenseMatrix(2, 2, new[] { 4.0, -2.0, -2.0, 4 - 0 }); // = (4 & -2 \\ -2 & 4)
var b = new[] { 6.0, 0.0 };
algorithm.Function = optimizer.Function.Create(A, b);
var actualArgMin = new double[2];
double actualMinimum;
var state = algorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedArgMin = new[] { -2.0, -1.0 };
var expectedMinimum = -6.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
Assert.That(actualArgMin, Is.EqualTo(expectedArgMin).AsCollection.Within(1E-7), String.Format("State: {0}; actual Minimum: {1}; expected Minimum: {2}; actual argMin: [{3}; {4}]; expected argMin: [{5}; {6}].", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin[0], expectedArgMin[1]));
}