/// <summary>
/// Find vector x that minimizes the function f(x), constrained within bounds, using the Broyden–Fletcher–Goldfarb–Shanno Bounded (BFGS-B) algorithm.
/// For more options and diagnostics consider to use <see cref="BfgsBMinimizer"/> directly.
/// </summary>
public static Vector <double> OfFunctionGradientConstrained(Func <Vector <double>, Tuple <double, Vector <double> > > functionGradient, Vector <double> lowerBound, Vector <double> upperBound, Vector <double> initialGuess, double gradientTolerance = 1e-5, double parameterTolerance = 1e-5, double functionProgressTolerance = 1e-5, int maxIterations = 1000)
{
var objective = ObjectiveFunction.Gradient(functionGradient);
var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
var result = algorithm.FindMinimum(objective, lowerBound, upperBound, initialGuess);
return(result.MinimizingPoint);
}
/// <summary>
/// Find vector x that minimizes the function f(x), constrained within bounds, using the Broyden–Fletcher–Goldfarb–Shanno Bounded (BFGS-B) algorithm.
/// The missing gradient is evaluated numerically (forward difference).
/// For more options and diagnostics consider to use <see cref="BfgsBMinimizer"/> directly.
/// </summary>
public static Vector <double> OfFunctionConstrained(Func <Vector <double>, double> function, Vector <double> lowerBound, Vector <double> upperBound, Vector <double> initialGuess, double gradientTolerance = 1e-5, double parameterTolerance = 1e-5, double functionProgressTolerance = 1e-5, int maxIterations = 1000)
{
var objective = ObjectiveFunction.Value(function);
var objectiveWithGradient = new Optimization.ObjectiveFunctions.ForwardDifferenceGradientObjectiveFunction(objective, lowerBound, upperBound);
var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
var result = algorithm.FindMinimum(objectiveWithGradient, lowerBound, upperBound, initialGuess);
return(result.MinimizingPoint);
}
public void Thurber_BfgsB_Dif()
{
var obj = ObjectiveFunction.NonlinearFunction(ThurberModel, ThurberX, ThurberY, accuracyOrder: 6);
var solver = new BfgsBMinimizer(1e-10, 1e-10, 1e-10, 1000);
var result = solver.FindMinimum(obj, ThurberLowerBound, ThurberUpperBound, ThurberStart);
for (int i = 0; i < result.MinimizingPoint.Count; i++)
{
AssertHelpers.AlmostEqualRelative(ThurberPbest[i], result.MinimizingPoint[i], 6);
}
}
public void FindMinimum_Rosenbrock_Easy_OneBoundary()
{
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
var solver = new BfgsBMinimizer(1e-5, 1e-5, 1e-5, maximumIterations: 1000);
var lowerBound = new DenseVector(new[] { 1.0, -5.0 });
var upperBound = new DenseVector(new[] { 5.0, 5.0 });
var initialGuess = new DenseVector(new[] { 1.2, 1.2 });
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
}
public void FindMinimum_Rosenbrock_MinimumLesserOrEqualToUpperBoundary()
{
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
var solver = new BfgsBMinimizer(1e-5, 1e-5, 1e-5, maximumIterations: 1000);
var lowerBound = new DenseVector(new[] { -2.0, -2.0 });
var upperBound = new DenseVector(new[] { 0.5, 0.5 });
var initialGuess = new DenseVector(new[] { -0.9, -0.5 });
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
Assert.LessOrEqual(result.MinimizingPoint[0], upperBound[0]);
Assert.LessOrEqual(result.MinimizingPoint[1], upperBound[1]);
}
public void FindMinimum_Quadratic_TwoBoundaries()
{
var obj = ObjectiveFunction.Gradient(
x => x[0] * x[0] + x[1] * x[1],
x => new DenseVector(new[] { 2 * x[0], 2 * x[1] })
);
var solver = new BfgsBMinimizer(1e-5, 1e-5, 1e-5, maximumIterations: 1000);
var lowerBound = new DenseVector(new[] { 1.0, 1.0 });
var upperBound = new DenseVector(new[] { 2.0, 2.0 });
var initialGuess = new DenseVector(new[] { 1.5, 1.5 });
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
Assert.That(Math.Abs(result.MinimizingPoint[1] - 1.0), Is.LessThan(1e-3));
}
public void Mgh_Tests(TestFunctions.TestCase test_case)
{
var obj = new MghObjectiveFunction(test_case.Function, true, true);
var solver = new BfgsBMinimizer(1e-8, 1e-8, 1e-8, 1000);
var result = solver.FindMinimum(obj, test_case.LowerBound, test_case.UpperBound, test_case.InitialGuess);
if (test_case.MinimizingPoint != null)
{
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
}
var val1 = result.FunctionInfoAtMinimum.Value;
var val2 = test_case.MinimalValue;
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
var abs_err = Math.Abs(val1 - val2);
var rel_err = abs_err / abs_min;
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
Assert.That(success, "Minimal function value is not as expected.");
}
public void BfgsMinimizer_MinimizesProperlyWhenConstrainedInOneVariable()
{
// Test comes from github issue 510
// https://github.com/mathnet/mathnet-numerics/issues/510
Func <Vector <double>, double> function = (Vector <double> vectorArg) =>
{
double x = vectorArg[0];
double y = -1.0 * Math.Exp(-x * x);
return(y);
};
double gradientTolerance = 1e-10;
double parameterTolerance = 1e-10;
double functionProgressTolerance = 1e-10;
int maxIterations = 1000;
var initialGuess = new DenseVector(new[] { -1.0 });
// Bad Bound
var lowerBound = new DenseVector(new[] { -2.0 });
var upperBound = new DenseVector(new[] { 2.0 });
var objective = ObjectiveFunction.Value(function);
var objectiveWithGradient = new ForwardDifferenceGradientObjectiveFunction(objective, lowerBound, upperBound);
var algorithm = new BfgsBMinimizer(gradientTolerance, parameterTolerance, functionProgressTolerance, maxIterations);
var result = algorithm.FindMinimum(objectiveWithGradient, lowerBound, upperBound, initialGuess);
var resultVector = result.MinimizingPoint;
double xResult = resultVector[0];
// (actual minimum at zero)
var abs_err = Math.Abs(xResult);
var success = abs_err < 1e-6;
Assert.That(success, "Minimal function value is not as expected.");
}