Add parameters constraints to Apache Math3 fitting

Question

I'm developing a fitting application using Apache commons math3. I have successfully created the ParametricUnivariateFunction

public class MyFunc implements ParametricUnivariateFunction {
@Override
public double value(double x, double... Parameters) {
    double m = parameters[0], k = parameters[1], b = parameters[2];
    return m * k * b * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1);
}
@Override
public double[] gradient(double x, double... Parameters) {
    final double m = parameters[0];
    final double k = parameters[1];
    final double b = parameters[2];
    return new double[]{
        b * k * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1),
        (b - 1) * b * k * m * x * Math.exp(-2 * k * x) * Math.pow(1 - Math.exp(-k * x), b - 2) + b * m * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1) - b * k * m * x * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1),
        k * m * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1) + b * k * m * Math.exp(-k * x) * Math.pow(1 - Math.exp(-k * x), b - 1) * Math.log(1 - Math.exp(-k * x))
    };
}

}

And the AbstractCurveFitter

public class MyFuncFitter extends AbstractCurveFitter {

@Override
protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points) {
    final int len = points.size();
    final double[] target = new double[len];
    final double[] weights = new double[len];
    final double[] initialGuess = {50, 1.0, 1.0};

    int i = 0;
    for (WeightedObservedPoint point : points) {
        target[i] = point.getY();
        weights[i] = point.getWeight();
        i += 1;
    }

    final AbstractCurveFitter.TheoreticalValuesFunction model = new AbstractCurveFitter.TheoreticalValuesFunction(new MyFunc(), points);

    return new LeastSquaresBuilder().
            maxEvaluations(Integer.MAX_VALUE).
            maxIterations(Integer.MAX_VALUE).
            start(initialGuess).
            target(target).
            weight(new DiagonalMatrix(weights)).
            model(model.getModelFunction(), model.getModelFunctionJacobian()).build();
}

}

And I use them in the main

public static void main(String[] args) {

    MyFuncFitter fitter = new MyFuncFitter();
    ArrayList<WeightedObservedPoint> points = new ArrayList<>();

    points.add(new WeightedObservedPoint(1.0, 0.25, 3.801713179));
    ///...
    points.add(new WeightedObservedPoint(1.0, 4, 10.46561902));

    final double coeffs[] = fitter.fit(points);
    System.out.println(Arrays.toString(coeffs));
}

This works very well!

Now I have to add constraints to the parameters (in particular m<=100, k>=0 e b>=1).

How can I add these constraints to the system above?

Answer 1

I found a solution: Use Java Optimization Modeler

OptimizationProblem op = new OptimizationProblem();
...
op.addDecisionVariable("m", false, new int[]{1, 1});
...
op.addConstraint("m<=100");//<- the constraints
...
op.setInitialSolution("m", 50);//optional
...
op.setObjectiveFunction("minimize", str);//where str is the string representing the function to minimize
...
System.loadLibrary("Ipopt38");
op.solve("ipopt");
...
if (!op.solutionIsOptimal()) {
        return null;
}

features[0] = op.getPrimalSolution("m").toValue();
...
features[3] = op.getOptimalCost();