public void NLoptTutorialExample_TestCaseNLoptConstraints_AnalyticSolution(NLoptAlgorithm nloptAlgorithm)
{
var multiDimOptimizer = new NLoptMultiDimOptimizer(NLoptAlgorithm.LN_COBYLA, NLoptAbortCondition.Create(relativeXTolerance: 1E-4));
var nloptBoxConstraint = multiDimOptimizer.Constraint.Create(MultiDimRegion.Interval.Create(dimension: 2, lowerBounds: new[] { Double.NegativeInfinity, 0.0 }, upperBounds: new[] { Double.PositiveInfinity, Double.PositiveInfinity }));
double a1 = 2.0;
double b1 = 0.0;
double a2 = -1;
double b2 = 1.0;
/* this code uses NLopt specific constraints: */
var optimizer = multiDimOptimizer.Create(nloptBoxConstraint,
multiDimOptimizer.Constraint.Create(2,
(x, grad) =>
{
if (grad != null)
{
grad[0] = 3.0 * a1 * (a1 * x[0] + b1) * (a1 * x[0] + b1);
grad[1] = -1.0;
}
return((a1 * x[0] + b1) * (a1 * x[0] + b1) * (a1 * x[0] + b1) - x[1]);
}),
multiDimOptimizer.Constraint.Create(2,
(x, grad) =>
{
if (grad != null)
{
grad[0] = 3.0 * a2 * (a2 * x[0] + b2) * (a2 * x[0] + b2);
grad[1] = -1.0;
}
return((a2 * x[0] + b2) * (a2 * x[0] + b2) * (a2 * x[0] + b2) - x[1]);
}
));
optimizer.Function = multiDimOptimizer.Function.Create(2, (x, grad) =>
{
if (grad != null)
{
grad[0] = 0.0;
grad[1] = 0.5 / Math.Sqrt(x[1]);
}
return(Math.Sqrt(x[1]));
});
var actualArgMin = new[] { 1.234, 5.678 };
double actualMinimum;
optimizer.FindMinimum(actualArgMin, out actualMinimum);
double expectedMinimum = Math.Sqrt(8.0 / 27.0);
double expectedArgMin0 = 1.0 / 3.0;
double expectedArgMin1 = 8.0 / 27.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-3));
Assert.That(actualArgMin[0], Is.EqualTo(expectedArgMin0).Within(1E-3));
Assert.That(actualArgMin[1], Is.EqualTo(expectedArgMin1).Within(1E-3));
}
public void FindMinimum_TestFunctionWithLinearConstraints_AnalyticResult()
{
/* Constraints:
* x_0 + x_1 + x_2 >= 6,
* -x_0 - x_1 + 2* x_2 >= 2,
* x_0, x_1, x_2 >= 0,
* */
// todo: this unit test failed; see
/* https://nlopt-discuss.ab-initio.mit.narkive.com/05OUy9nv/net-wrapper-vector-valued-constraints
*
* see also comments in: NLoptConstraintFactory.Create(MultiDimRegion.LinearInequality linearInequalityConstraint)
*/
var optimizer = new NLoptMultiDimOptimizer(NLoptAlgorithm.LN_COBYLA);
//var optimizer = new NLoptMultiDimOptimizer(NLoptAlgorithm.LD_MMA);
var boxConstraint = optimizer.Constraint.Create(MultiDimRegion.Interval.Create(3, new[] { 0.0, 0.0, 0.0 }, new[] { Double.NaN, Double.NaN, Double.NaN }));
var inequalityConstraint = optimizer.Constraint.Create(MultiDimRegion.LinearInequality.Create(new DenseMatrix(3, 2, new[] { 1.0, 1.0, 1.0, -1.0, -1.0, 2.0 }), new[] { 6.0, 2.0 }));
var algorithm = optimizer.Create(boxConstraint, inequalityConstraint);
var A = new DenseMatrix(3, 3, new[] { 2.0, 1.0, 0.0, 1.0, 4.0, 2.0, 0.0, 2.0, 4.0 });
var b = new[] { 4.0, 6.0, 12.0 };
algorithm.SetFunction( // a simple quadratic program
(x, grad) =>
{
if (grad != null)
{
}
return(0.5 * DenseMatrix.GetBilinearForm(A, x) + BLAS.Level1.ddot(3, x, b));
});
var actualArgMin = new[] { 3.3333, 0.0001, 2.66 };
double actualMinimum;
var state = algorithm.FindMinimum(actualArgMin, out actualMinimum);
var expectedArgMin = new[] { 3 + 1.0 / 3.0, 0.0, 2 + 2.0 / 3.0 };
var expectedMinimum = 70.666666666666666;
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 NLoptCobyla_TestCase_AnalyticMinimum()
{
var cobyla = new NLoptMultiDimOptimizer(NLoptAlgorithm.LN_COBYLA);
var nloptBoxConstraint = cobyla.Constraint.Create(MultiDimRegion.Interval.Create(dimension: 2, lowerBounds: new[] { 1.0, 5.0 }, upperBounds: new[] { 12.4, 34.2 }));
var algorithm = cobyla.Create(nloptBoxConstraint);
algorithm.Function = cobyla.Function.Create(2, x => x[0] * x[0] + x[1] * x[1] + 1.123);
double[] argMin = new double[2] {
1.4, 5.8
};
double actual;
var code = algorithm.FindMinimum(argMin, out actual);
double expected = 1.0 * 1.0 + 5.0 * 5.0 + 1.123;
Assert.That(actual, Is.EqualTo(expected).Within(1E-7));
}
public void NLoptTutorialExample_TestCase_AnalyticSolution(NLoptAlgorithm nloptAlgorithm)
{
var multiDimOptimizer = new NLoptMultiDimOptimizer(nloptAlgorithm, NLoptAbortCondition.Create(relativeXTolerance: 1E-4));
var nloptBoxConstraint = multiDimOptimizer.Constraint.Create(MultiDimRegion.Interval.Create(dimension: 2, lowerBounds: new[] { Double.NegativeInfinity, 0.0 }, upperBounds: new[] { Double.PositiveInfinity, Double.PositiveInfinity }));
double a1 = 2.0;
double b1 = 0.0;
/* This code uses generic constraints, i.e. polynomial constraints: */
/* The constraints in the Tutorial of the NLopt documentation can be re-written as polynomial in the following form:
*
* x_2 - a^3 * x_1^3 - 3*a^2*b*x_1^2 - 3*a*b^2 * x_1 >= b^3
*/
var polynomialConstraint1 = MultiDimRegion.Polynomial.Create(2, b1 * b1 * b1, Double.PositiveInfinity, new[] {
1.0, -a1 * a1 * a1, -3.0 * a1 * a1 * b1, -3.0 * a1 * b1 * b1
},
MultiDimRegion.Polynomial.Monomial.Create(1, 1),
MultiDimRegion.Polynomial.Monomial.Create(0, 3),
MultiDimRegion.Polynomial.Monomial.Create(0, 2),
MultiDimRegion.Polynomial.Monomial.Create(0, 1));
double a2 = -1;
double b2 = 1.0;
var polynomialConstraint2 = MultiDimRegion.Polynomial.Create(2, b2 * b2 * b2, Double.PositiveInfinity, new[] {
1.0, -a2 * a2 * a2, -3.0 * a2 * a2 * b2, -3.0 * a2 * b2 * b2
},
MultiDimRegion.Polynomial.Monomial.Create(1, 1),
MultiDimRegion.Polynomial.Monomial.Create(0, 3),
MultiDimRegion.Polynomial.Monomial.Create(0, 2),
MultiDimRegion.Polynomial.Monomial.Create(0, 1));
var optimizer = multiDimOptimizer.Create(nloptBoxConstraint,
multiDimOptimizer.Constraint.Create(polynomialConstraint1),
multiDimOptimizer.Constraint.Create(polynomialConstraint2));
optimizer.Function = multiDimOptimizer.Function.Create(2, (x, grad) =>
{
if (grad != null)
{
grad[0] = 0.0;
grad[1] = 0.5 / Math.Sqrt(x[1]);
}
return(Math.Sqrt(x[1]));
});
var actualArgMin = new[] { 1.234, 5.678 };
double actualMinimum;
var state = optimizer.FindMinimum(actualArgMin, out actualMinimum);
double expectedMinimum = Math.Sqrt(8.0 / 27.0);
double expectedArgMin0 = 1.0 / 3.0;
double expectedArgMin1 = 8.0 / 27.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-3), String.Format("<Minimum> State: {0}; Actual minimum: {1}; Expected minimum: {2}; Actual argMin: ({3}; {4}); Expected argMin: ({5}; {6})", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin0, expectedArgMin1));
Assert.That(actualArgMin[0], Is.EqualTo(expectedArgMin0).Within(1E-3), String.Format("<argMin[0]> State: {0}; Actual minimum: {1}; Expected minimum: {2}; Actual argMin: ({3}; {4}); Expected argMin: ({5}; {6})", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin0, expectedArgMin1));
Assert.That(actualArgMin[1], Is.EqualTo(expectedArgMin1).Within(1E-3), String.Format("<argMin[1]> State: {0}; Actual minimum: {1}; Expected minimum: {2}; Actual argMin: ({3}; {4}); Expected argMin: ({5}; {6})", state, actualMinimum, expectedMinimum, actualArgMin[0], actualArgMin[1], expectedArgMin0, expectedArgMin1));
}