Example 3: Minimum of a multivariate function

import com.imsl.math.*;

public class MinUnconMultiVarEx3 {

    static class MyFunction implements MinUnconMultiVar.Hessian {

        public double f(double[] x) {
            return 100. * ((x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0]))
                    + (1. - x[0]) * (1. - x[0]);
        }

        public void gradient(double[] x, double[] gp) {
            gp[0] = -400. * (x[1] - x[0] * x[0]) * x[0] - 2. * (1. - x[0]);
            gp[1] = 200. * (x[1] - x[0] * x[0]);
        }

        public void hessian(double[] x, double[][] hess) {
            hess[0][0] = -4.e2 * x[1] + 1.2e3 * x[0] * x[0] + 2.e0;
            hess[1][0] = -4.e2 * x[0];
            hess[0][1] = hess[1][0];
            hess[1][1] = 2.e2;
        }
    }

    public static void main(String args[]) throws Exception {
        MinUnconMultiVar solver = new MinUnconMultiVar(2);
        solver.setGuess(new double[]{-1.2, 1.0});
        double x[] = solver.computeMin(new MyFunction());
        System.out.println("Minimum point is (" + x[0] + ", " + x[1] + ")");
    }
}

Output

Minimum point is (1.0000000139452756, 1.0000000143547352)