Example 3: Solve a Quadratic Programming Problem with Inconsistent System Constraints

In the quadratic programming problem variables 2 and 6 are fixed at the value zero by the equality constraints. The inequalities propose that the sums of the variables are at least 5.1 and no more than 4.9. These last two are inconsistent conditions, causing the InconsistentSystemException to be thrown.

import com.imsl.math.*;

public class QuadraticProgrammingEx3 {

    public static void main(String[] args) {

        double[][] h = {
            {2.000, 0.000, 0.000, 0.000, 0.000, 0.000},
            {0.000, 2.000, 0.000, 0.000, 0.000, 0.000},
            {0.000, 0.000, 2.000, 0.000, 0.000, 0.000},
            {0.000, 0.000, 0.000, 2.000, 0.000, 0.000},
            {0.000, 0.000, 0.000, 0.000, 2.000, 0.000},
            {0.000, 0.000, 0.000, 0.000, 0.000, 2.000}
        };
        double[] g = {5.000, 5.000, 5.000, 5.000, 5.000, 5.000};

        double[][] aEquality = {
            {0.000, 1.000, 0.000, 0.000, 0.000, 0.000},
            {0.000, 0.000, 0.000, 0.000, 0.000, 1.000}
        };
        double[] bEquality = {0.000, 0.000};

        double[][] aInequality = {
            {1.000, 1.000, 1.000, 1.000, 1.000, 1.000},
            {-1.000, -1.000, -1.000, -1.000, -1.000, -1.000}
        };
        double delta = 0.1;  // change to 0.0 to pass
        double[] bInequality = {5 + delta, -5 + delta};
      
        try {
            QuadraticProgramming qp =
                    new QuadraticProgramming(h, g, aEquality, bEquality,
                    aInequality, bInequality);
            double x[] = qp.getSolution();
            new com.imsl.math.PrintMatrix("Solution").print(x);
        } catch (Exception e) {
            System.out.println("No solution for the LP problem was found. " + 
                    "All constraints are not\nsatisfied. L1 minimization " + 
                    "was applied to all constraints (including\nbounds and" +
                    "simple variables) but the equalities, to approximate\n" +
                    "violated non-equalities as well as possible.  If a " +
                    "feasible\nsolution is possible then try using " +
                    "refinement.");
        }
    }
}

Output

No solution for the LP problem was found. All constraints are not
satisfied. L1 minimization was applied to all constraints (including
bounds andsimple variables) but the equalities, to approximate
violated non-equalities as well as possible.  If a feasible
solution is possible then try using refinement.