package com.imsl.test.example.math;

import com.imsl.math.*;
import com.imsl.stat.*;

/**
 * <p>
 * Solves a constrained optimization problem using a direct search complex
 * method.
 * </p>
 * <p>
 * The constrained problem
 * $$ \min f(x_1,x_2) = 100.0(x_2-x_1^2)^2 + (1.0-x_1)^2 \\
 * \text{subject to} \quad
 * \begin{array}{l}
 *    -2 \le x_1 \le 0.5 \\
 *    -1 \le x_2 \le 2
 * \end{array} $$
 * is solved with an initial guess \((-1.2,1.0)\) and the solution is printed.
 * The analytical solution is \((x_1,x_2) = (0.5,0.25)\) with optimum value
 * \(0.25\).
 * </p>
 *
 * @see <a href="NelderMeadEx2.java">Code</a>
 * @see <a href="doc-files/NelderMeadEx2.out">Output</a>
 */
public class NelderMeadEx2 {

    public static void main(String args[]) {
        NelderMead.Function fcn = new NelderMead.Function() {
            public double f(double x[]) {
                double fValue;
                double t1 = x[1] - x[0] * x[0];
                double t2 = 1.0 - x[0];
                fValue = 100.0 * t1 * t1 + t2 * t2;

                return fValue;
            }
        };

        double ftol = 1.0e-7;
        // The initial guess is used as the first vertex of the random
        // initial complex.
        double xguess[] = {-1.2, 1.0};
        double xlb[] = {-2.0, -1.0};
        double xub[] = {0.5, 2.0};
        // Define random object that is used internally in the computation
        // of the initial complex.
        Random r = new com.imsl.stat.Random(123457);
        r.setMultiplier(16807);

        NelderMead zs = new NelderMead(fcn, xlb, xub);
        zs.setTolerance(ftol);
        zs.setRandomObject(r);
        zs.setGuess(xguess);
        zs.solve();

        double[] sol = zs.getSolution();
        double obj = zs.getObjectiveValue();

        System.out.println("Solution:");
        for (int k = 0; k < sol.length; k++) {
            System.out.println("x[" + k + "] = " + sol[k]);
        }
        System.out.println();
        System.out.println("Optimum value: " + obj);
    }
}