QC seems not work

[shouriken]

Hello, I have a problem for Markowitz max-return model.

$$ \begin{align*} \text{maximize} \quad & expectRreturn \cdot w \\ \text{subject to} \quad & \sqrt{w^T \Sigma w} \le specificRisk \end{align*} $$

and, there are some simple range constraints for some assets.
core code:

Expression riskVariance = model.newExpression("risk");
riskVariance.setQuadraticFactors(x, covars);
riskVariance.upper(risk * risk);

Expression optimisationReturn = model.addExpression("expectedReturn").weight(1.0);
for (int i = 0; i < expectedReturn.length; i++) {
    optimisationReturn.set(x.get(i), expectedReturn[i]);
}
model.maximise();

double[] res = new double[x.size()];
Array1D<BigDecimal> point = Array1D.R256.make(x.size());
for (int i = 0; i < x.size(); i++) {
    res[i] = x.get(i).getValue().doubleValue();
    point.set(i, x.get(i).getValue());
}
System.out.println(riskVariance.evaluate(point));

I take the result of model back to risk QC, the riskVariance.evaluate(point) is great than $risk^2$. Then I change the value of risk, but the result doesn't changed.

If I use the QC incorrectly? If the QC doesn't work?

[apete]

None of the built-in solvers in ojAlgo can handle quadratic constraints.

You have to either use a third party solver: https://www.ojalgo.org/2025/02/hooking-your-solver-to-ojalgo/

or model the problem differently. One way is to relax the variance expression and make it part of the objective function balanced with the return expression. This is what's done in the org.ojalgo.data.domain.finance.portfolio.MarkowitzModel.

[shouriken]

ok, thanks for your attention and reply.