public static ScalarMinimizationResult Minimum(IScalarObjectiveFunction objective, double lowerBound, double upperBound, double xTolerance = 1e-5, int maxIterations = 1000)
{
if (upperBound <= lowerBound)
{
throw new OptimizationException("Lower bound must be lower than upper bound.");
}
double middlePointX = lowerBound + (upperBound - lowerBound) / (1 + Constants.GoldenRatio);
IScalarObjectiveFunctionEvaluation lower = objective.Evaluate(lowerBound);
IScalarObjectiveFunctionEvaluation middle = objective.Evaluate(middlePointX);
IScalarObjectiveFunctionEvaluation upper = objective.Evaluate(upperBound);
ValueChecker(lower.Value, lowerBound);
ValueChecker(middle.Value, middlePointX);
ValueChecker(upper.Value, upperBound);
int iterations = 0;
while (Math.Abs(upper.Point - lower.Point) > xTolerance && iterations < maxIterations)
{
double testX = lower.Point + (upper.Point - middle.Point);
var test = objective.Evaluate(testX);
ValueChecker(test.Value, testX);
if (test.Point < middle.Point)
{
if (test.Value > middle.Value)
{
lower = test;
}
else
{
upper = middle;
middle = test;
}
}
else
{
if (test.Value > middle.Value)
{
upper = test;
}
else
{
lower = middle;
middle = test;
}
}
iterations += 1;
}
if (iterations == maxIterations)
{
throw new MaximumIterationsException("Max iterations reached.");
}
return(new ScalarMinimizationResult(middle, iterations, ExitCondition.BoundTolerance));
}
public static ScalarMinimizationResult Minimum(IScalarObjectiveFunction objective, double lowerBound, double upperBound, double xTolerance = 1e-5, int maxIterations = 1000, int maxExpansionSteps = 10, double lowerExpansionFactor = 2.0, double upperExpansionFactor = 2.0)
{
if (upperBound <= lowerBound)
{
throw new OptimizationException("Lower bound must be lower than upper bound.");
}
double middlePointX = lowerBound + (upperBound - lowerBound) / (1 + Constants.GoldenRatio);
IScalarObjectiveFunctionEvaluation lower = objective.Evaluate(lowerBound);
IScalarObjectiveFunctionEvaluation middle = objective.Evaluate(middlePointX);
IScalarObjectiveFunctionEvaluation upper = objective.Evaluate(upperBound);
ValueChecker(lower.Value);
ValueChecker(middle.Value);
ValueChecker(upper.Value);
int expansionSteps = 0;
while ((expansionSteps < maxExpansionSteps) && (upper.Value < middle.Value || lower.Value < middle.Value))
{
if (lower.Value < middle.Value)
{
lowerBound = 0.5 * (upperBound + lowerBound) - lowerExpansionFactor * 0.5 * (upperBound - lowerBound);
lower = objective.Evaluate(lowerBound);
}
if (upper.Value < middle.Value)
{
upperBound = 0.5 * (upperBound + lowerBound) + upperExpansionFactor * 0.5 * (upperBound - lowerBound);
upper = objective.Evaluate(upperBound);
}
middlePointX = lowerBound + (upperBound - lowerBound) / (1 + Constants.GoldenRatio);
middle = objective.Evaluate(middlePointX);
expansionSteps += 1;
}
if (upper.Value < middle.Value || lower.Value < middle.Value)
{
throw new OptimizationException("Lower and upper bounds do not necessarily bound a minimum.");
}
int iterations = 0;
while (Math.Abs(upper.Point - lower.Point) > xTolerance && iterations < maxIterations)
{
// Recompute middle point on each iteration to avoid loss of precision
middlePointX = lower.Point + (upper.Point - lower.Point) / (1 + Constants.GoldenRatio);
middle = objective.Evaluate(middlePointX);
ValueChecker(middle.Value);
double testX = lower.Point + (upper.Point - middle.Point);
var test = objective.Evaluate(testX);
ValueChecker(test.Value);
if (test.Point < middle.Point)
{
if (test.Value > middle.Value)
{
lower = test;
}
else
{
upper = middle;
}
}
else
{
if (test.Value > middle.Value)
{
upper = test;
}
else
{
lower = middle;
}
}
iterations += 1;
}
if (iterations == maxIterations)
{
throw new MaximumIterationsException("Max iterations reached.");
}
return(new ScalarMinimizationResult(middle, iterations, ExitCondition.BoundTolerance));
}