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));
}
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));
}