public void FindMinimum_BettsTestFunction_AnalyticResult()
{
/* f(x) = 0.01 * x_0^2 + x_1^2 w.r.t 10*x_0 - x_1 >= 10, 2 <= x_0 <= 50, -50 <= x_1 <= 50 */
var optimizer = new LevenbergMarquardtOptimizer();
var box = MultiDimRegion.Interval.Create(2, new[] { 2.0, -50.0 }, new[] { 50.0, 50.0 });
var linConstraint = new MultiDimRegion.LinearInequality(new DenseMatrix(2, 1, new[] { 10.0, -1.0 }), new[] { 10.0 });
var algorithm = optimizer.Create(optimizer.Constraint.Create(box), optimizer.Constraint.Create(linConstraint));
algorithm.Function = optimizer.Function.Create(2, 2,
(x, J, y) =>
{
if (J != null)
{
J[0] = 0.01;
J[1] = 0.0;
J[2] = 0.0;
J[3] = 1.0;
}
y[0] = 0.1 * x[0];
y[1] = x[1];
});
var actualArgMin = new[] { 4.0, 5.0 }; // use feasible initial points
var state = algorithm.FindMinimum(actualArgMin, out double actualMinimum);
var expectedArgMin = new[] { 2.0, 0.0 };
var expectedMinimum = 0.04;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-5), 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-5), 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_SimpBiggsTestFunction_AnalyticResult()
{
var optimizer = new LevenbergMarquardtOptimizer();
var algorithm = optimizer.Create(optimizer.Constraint.Create(MultiDimRegion.Interval.Create(2, new[] { 1.0, 0.0 }, new[] { Double.PositiveInfinity, Double.PositiveInfinity })));
algorithm.Function = optimizer.Function.Create(2, 2,
(x, J, y) =>
{
if (J != null)
{
J[0] = 1.0;
J[1] = 0.0;
J[2] = 0.0;
J[3] = 1.0;
}
y[0] = x[0] - 5.0;
y[1] = x[1];
});
var actualArgMin = new[] { 3.1, 1.2 }; // not feasible
var state = algorithm.FindMinimum(actualArgMin, out double actualMinimum);
var expectedArgMin = new[] { 5.0, 0.0 };
var expectedMinimum = 0.0;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-5), 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-5), 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_SimpleTestFunction_AnalyticResult()
{
var optimizer = new LevenbergMarquardtOptimizer();
var algorithm = optimizer.Create(2);
algorithm.Function = optimizer.Function.Create(2, 3,
(x, J, y) =>
{
if (J != null)
{
J[0] = -4 + 2 * x[0];
J[1] = -6 + 2 * x[0];
J[2] = -8 + 2 * x[0];
J[3] = 4 * Math.Exp(4 * x[1]);
J[4] = 13 * Math.Exp(13 * x[1]);
J[5] = 16 * Math.Exp(16 * x[1]);
}
y[0] = Math.Pow(2.0 - x[0], 2) + Math.Exp(x[1] * 4) - 5.0;
y[1] = Math.Pow(3.0 - x[0], 2) + Math.Exp(x[1] * 13) - 5.0;
y[2] = Math.Pow(4.0 - x[0], 2) + Math.Exp(x[1] * 16) - 5.0;
});
var actualArgMin = new[] { 4.0, 0.0 };
var state = algorithm.FindMinimum(actualArgMin, out double actualMinimum);
var expectedArgMin = new[] { 3.915042527, 0.1029172979 };
var expectedMinimum = 0.19361117440123918;
Assert.That(actualMinimum, Is.EqualTo(expectedMinimum).Within(1E-5), 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-5), 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]));
}
/// <summary>Initializes a new instance of the <see cref="Algorithm"/> class.
/// </summary>
/// <param name="optimizer">The <see cref="LevenbergMarquardtOptimizer"/> object that serves as factory of the current object.</param>
/// <param name="constraints">A collection of contraints for the optimization algorithm represented by the current instance, where each constraint has been created via a specific function of property <see cref="MultiDimOptimizer.Constraint"/>.</param>
internal Algorithm(LevenbergMarquardtOptimizer optimizer, IConstraint[] constraints)
{
m_Optimizer = optimizer ?? throw new ArgumentNullException(nameof(optimizer));
/* each constraint should be specified in its MultiDimOptimizerConstraint representation which contains the RegionRepresentation */
m_ProjectionOntoFeasibleSet = FeasibleSetProjection.Create(constraints.Cast <MultiDimOptimizerConstraint>().Select(x => x.RegionRepresentation), new GoldfarbIdanaQuadraticProgram());
}
/// <summary>Initializes a new instance of the <see cref="Algorithm"/> class.
/// </summary>
/// <param name="optimizer">The <see cref="LevenbergMarquardtOptimizer"/> object that serves as factory of the current object.</param>
/// <param name="dimension">The dimension of the feasible region.</param>
internal Algorithm(LevenbergMarquardtOptimizer optimizer, int dimension)
{
m_Optimizer = optimizer ?? throw new ArgumentNullException(nameof(optimizer));
if (dimension <= 0)
{
throw new ArgumentOutOfRangeException(nameof(dimension));
}
m_ProjectionOntoFeasibleSet = FeasibleSetProjection.Create(dimension);
}
/// <summary>Initializes a new instance of the <see cref="Algorithm"/> class.
/// </summary>
/// <param name="optimizer">The <see cref="LevenbergMarquardtOptimizer"/> object that serves as factory of the current object.</param>
/// <param name="boxConstraints">The box constraints.</param>
internal Algorithm(LevenbergMarquardtOptimizer optimizer, MultiDimRegion.Interval boxConstraints)
{
m_Optimizer = optimizer ?? throw new ArgumentNullException(nameof(optimizer));
m_ProjectionOntoFeasibleSet = FeasibleSetProjection.Create(boxConstraints);
}