Question

I tried solving the following problem using the SuanShu optimization library, with no success.

The optimization problem is:

Find the largest integral h such that the following constraint holds:

(h-2) * ArithmeticUtils.binomialCoefficient(b+h-2, h-1) -
        ArithmeticUtils.binomialCoefficient(b+h-3, h-3) +
        ArithmeticUtils.binomialCoefficientDouble(b+h-3,h-2)
        - 2*epsilon*N

where b,epsilon, N are given and they are int, double, int respectively.

Can you please tell me which optimizer I should use and what optimization function ?

The code up to now looks like this:

    public void optimize(){
            //create the univariate function to be optimized
    UnivariateRealFunction functionToOptimize = new UnivariateRealFunction() {

        @Override
        public double evaluate(double h) {
            return -h;
        }
    };
    UnivariateRealFunction hConstraint = new UnivariateRealFunction() {

        public double evaluate(double h) {
                          (h-2) * ArithmeticUtils.binomialCoefficient(b+h-2, h-1) -
                                  ArithmeticUtils.binomialCoefficient(b+h-3, h-3) +
                                  ArithmeticUtils.binomialCoefficientDouble(b+h-3,h-2)
                                  - 2*epsilon*N
        }
    };

    List<RealScalarFunction> constraints = new ArrayList<RealScalarFunction>();
    constraints.add(hConstraint);

    ConstrainedOptimProblem problem = new ConstrainedOptimProblem(
            functionToOptimize, 
            null, 
            new GeneralLessThanConstraints(constraints));

    BFGS bfgs = new BFGS();

    PenaltyMethodMinimizer optim = new PenaltyMethodMinimizer(
            PenaltyMethodMinimizer.DEFAULT_PENALTY_FUNCTION_FACTORY, 
            1e30,
            bfgs);

    optim.solve(problem,1e-3,200);

    Vector xmin = optim.search(new DenseVector(new int[]{8}));
    double fxmin = functionToOptimize.evaluate(xmin.get(1));    
    System.out.println("fxmin: "+fxmin);
    System.out.println(String.format("f(%s) = %f",
            DoubleUtils.doubleArray2StringArray(xmin.toArray()), fxmin));

    }

I took a look at the Apache commons math library and I don’t have a clue on how to use it for this problem.

Answer 1

If you use SuanShu, you can try the brute force minimizer or DeOptim. For DeOptim, you need to code up your integral constraint cell factory, such as this: IntegralCellFactory.java