向Apache Math3拟合中添加参数约束

Question

我正在使用Apache开发一个合适的应用程序。我已经成功地创建了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))
    };
}

}

和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();
}

}

我主要是用它们

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));
}

这个很好用！

现在，我必须向参数添加约束(特别是m<=100，k>=0 e b>=1)。

如何将这些约束添加到上面的系统中？

Answer 1

我找到了一个解决方案:使用Java优化模型

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();