package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a quadratic programming problem in 4 variables.</p>
 * <p>
 * The quadratic programming problem is to minimize</p>
 *
 * <p>
 * $$x_0^2 + x_1^2 + x_2^2 + x_3^2 + x_4^2 - 2x_1x_2 - 2x_3x_4 - 2x_0$$</p>
 * <p>
 * subject to</p>
 *
 * <p>
 * $$x_0 + x_1 + x_2 + x_3 + x_4 = 5$$</p>
 *
 * <p>
 * $$x_2 - 2x_3 - 2x_4 = -3$$</p>
 *
 *
 * @see <a href="QuadraticProgrammingEx1.java">Code</a>
 * @see <a href="doc-files/QuadraticProgrammingEx1.out">Output</a>
 */
public class QuadraticProgrammingEx1 {

    public static void main(String args[]) throws Exception {
        double h[][] = {
            {2, 0, 0, 0, 0},
            {0, 2, -2, 0, 0},
            {0, -2, 2, 0, 0},
            {0, 0, 0, 2, -2},
            {0, 0, 0, -2, 2}
        };
        double aeq[][] = {
            {1, 1, 1, 1, 1},
            {0, 0, 1, -2, -2}
        };
        double beq[] = {5, -3};
        double g[] = {-2, 0, 0, 0, 0};

        QuadraticProgramming qp
                = new QuadraticProgramming(h, g, aeq, beq, null, null);
        // Print the solution and its dual
        new PrintMatrix("x").print(qp.getSolution());
        new PrintMatrix("dual").print(qp.getDual());
    }
}