package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Minimizes a nonlinear function with constraints.</p>
 * The problem
 * <p>
 * $${\rm {min}} \,\, f(x) = -x_0x_1x_2$$</p>
 * <p>
 * subject to</p>
 * 
 * $$\begin{array}{c}
 * -x_0 - 2x_1 -2x_2 \le 0 \\
 * x_0 + 2x_1 + 2x_2 \le 72 \\
 * 0 \le x_0 \le 20 \\
 * 0 \le x_1 \le 11 \\
 * 0 \le x_2 \le 42 \\
 * \end{array}$$
 * <p>
 * is solved with an initial guess of \( x_0 = 10 \),
 * \( x_1 = 10 \) and \( x_2 = 10 \).</p>
 *
 * @see <a href="MinConGenLinEx2.java">Code</a>
 * @see <a href="doc-files/MinConGenLinEx2.out">Output</a>
 */
public class MinConGenLinEx2 {

    public static void main(String args[]) throws Exception {
        int neq = 0;
        int ncon = 2;
        int nvar = 3;
        double a[] = {-1.0, -2.0, -2.0, 1.0, 2.0, 2.0};
        double xlb[] = {0.0, 0.0, 0.0};
        double xub[] = {20.0, 11.0, 42.0};
        double xguess[] = {10.0, 10.0, 10.0};
        double b[] = {0.0, 72.0};

        MinConGenLin.Gradient grad = new MinConGenLin.Gradient() {
            public double f(double[] x) {
                return -x[0] * x[1] * x[2];
            }

            public void gradient(double[] x, double[] g) {
                g[0] = -x[1] * x[2];
                g[1] = -x[0] * x[2];
                g[2] = -x[0] * x[1];
            }
        };

        MinConGenLin zf
                = new MinConGenLin(grad, nvar, ncon, neq, a, b, xlb, xub);

        zf.setGuess(xguess);
        zf.solve();
        new PrintMatrix("Solution").print(zf.getSolution());
        System.out.println("Objective value = " + zf.getObjectiveValue());
    }
}