[ojAlgo-user] Probably User Error, but...

[Greg S. <gs...@ho...>]

Hi, 

I have a very simple quadratic programming problem. In one degenerate case, the Q matrix is composed of zeroes. In other words, the problem is a linear programming problem with Equality and Inequality constraints. It seems like ConvexSolver should be able to solve the problem but it fails in somewhat interesting ways. I am not sure what I am doing wrong. 

I am minimizing the expression 

x' Q x' - c' x

where c = { 0.12, -0.05, 0.08, 0.07 }

I would expect that without an constraints, the solver should fail as it attempts to take x[0],x[2],x[3] to +infinity and x[1] to -infinity. I next set liberal constraints of +/- 99999 for all the factors. I would expect the solver to take the x vector to the bounds and terminate gracefully. In either case, the results are hard to understand. 

In the case where I use the zero matrix for Q, I get an infeasibility failure. Failure State = INVALID


In the case where I use an identity matrix (which is PSD and nice) , I get the result as:
x[0] = 0.12
x[1] = -0.05
x[2] = 0.08
x[3] = 0.07

In the case of zero matrix and constraints I get:

x[0] = 0.25
x[1] = 0.25
x[2] = 0.25
x[3] = 0.25

The for the case of an identity matrix and constraints I get

Identity Q matrix and  constraints -------------------------!
Initial solution: [0.12, -0.05, 0.08, 0.07]
Initial I-included-slack: []
Initial I-excluded-slack: [99999.12, 99998.95, 99999.08, 99999.07, 99998.88, 99999.05, 99998.92, 99998.93]

PerformIteration
Last Incl/Excl: -1/-1 => [] / [0, 1, 2, 3, 4, 5, 6, 7]
X/L: true X=[0.0, 0.0, 0.0, 0.0] L=[]
Current: [0.12, -0.05, 0.08, 0.07]
Step: [0.0, 0.0, 0.0, 0.0]
java.lang.NullPointerException


Any thoughts would be appreciated. Thank you to the creators of OjAlgo. It looks like a complete package!


-Greg


Test code below. 

public static void attempt5(boolean identity, boolean addDummyConstraints) {
        if (!identity && !addDummyConstraints) {
            System.out.println("Zero Q matrix and no constraints -------------------------!");
        } else if (!identity) {
            System.out.println("Zero Q matrix and constraints -------------------------!");
        } else if (!addDummyConstraints) {
            System.out.println("Identity Q matrix and no constraints -------------------------!");
        } else {
            System.out.println("Identity Q matrix and  constraints -------------------------!");
        }

        double[] C = new double[]{0.12, -0.05, 0.08, 0.07};
        final RawStore cov = new RawStore(4, 4);
        if (identity) {
            for (int i = 0; i < 4; i++) {
                cov.set(i, i, 1.0);
            }
        }
        final RawStore linPart = new RawStore(C, 4);
        ConvexSolver.Builder builder = ConvexSolver.getBuilder(
                cov,
                linPart);

        if (addDummyConstraints) {
            RawStore ineq = RawStore.FACTORY.rows(
                    new double[][]{{-1.0, 0.0, 0.0, 0.0}, {0.0, -1.0, 0.0, 0.0}, {0.0, 0.0, -1.0, 0.0}, {0.0, 0.0, 0.0, -1.0},
                    {1.0, 0.0, 0.0, 0.0}, {0.0, 1.0, 0.0, 0.0}, {0.0, 0.0, 1.0, 0.0}, {0.0, 0.0, 0.0, 1.0}});

            RawStore coeff = RawStore.FACTORY.columns(new double[][]{{99999, 99999, 99999, 99999, 99999, 99999, 99999, 99999}});

            builder = builder.inequalities(ineq, coeff);
        }
        final Optimisation.Options opts = new Optimisation.Options();
        opts.iterations_abort = 10000;
        opts.iterations_suffice = 100;
        opts.debug(ConvexSolver.class);
        final ConvexSolver cs = builder.build(opts);

        try {
            final Optimisation.Result solution = cs.solve();
            if (solution.getState() == Optimisation.State.DISTINCT
                    || solution.getState() == Optimisation.State.APPROXIMATE
                    || solution.getState() == Optimisation.State.OPTIMAL) {
                double[] pt = new double[4];
                for (int i = 0; i < pt.length; i++) {
                    pt[i] = solution.doubleValue(i);
                }

                System.out.println("Objective " + solution.getValue());
                for (int ii = 0; ii < 4; ii++) {
                    System.out.println("x[" + ii + "] = " + solution.doubleValue(ii));
                }
            } else {
                System.out.println("Failure State = " + solution.getState().name());

            }

        } catch (Exception e) {
            System.out.println(e);
        }
    }