[ojAlgo-user] using quadratic solver

[David J. <dav...@bu...>]

Hi, I'm new to ojalgo, and trying to work out the exact syntax needed to
configure the quadratic solver.

Specifically, I'm trying to solve a standard quadratic minimization problem:
min(1/2*transpose(alpha)*H*alpha - sum(alpha)), given 0 <= alphai <= C
(where C is a constant), for each element in alpha.  Alpha will be
initialized to 0s (or uninitialized, if no initial input is needed) and H to
a given input matrix.  I'm unclear on exactly what I need to configure in
the QuadraticExpressionsModel versus what is handled by the builder.  I also
can't seem to find a current example of how to configure an expression-based
model (except for the one in MarkowitzModel, which helped, but didn't
entirely clarify the logic).

My current (very rough) code skeleton looks like this:

final Variable[] vars = new Variable[2];
        vars[0] = new Variable("alpha");
        vars[0].setLowerLimit(new BigDecimal(0));
        vars[0].setUpperLimit(new BigDecimal(C));
        vars[0].setContributionWeight(BigMath.ONE);
        vars[1] = new Variable("H");

        final QuadraticExpressionsModel qem = new
QuadraticExpressionsModel(vars);
        qem.setMinimisation(true);

        final QuadraticSolver.Builder build = new
QuadraticSolver.Builder(qem);

I can't tell if alpha and H should even be listed as variables (as opposed
to expressions), how to associate my input matrices with them if they should
be, and how to describe range limits on alpha if they should not.  I'm also
not certain how to define my objective function - is the basic format
handled by the builder, or do I need to describe it in the model somehow?
Should I be using the inequalities(...) and objective(...) functions in the
builder, or defining those via the model?

Also, I know I can represent sum(alpha) in my equation by just setting C
(the vector in the basic equation format, not my constant) to be a singular
1 vector, but is there any way to ensure that the solver will then treat C
as a constant?

Thanks
David Johnson