QP and constraints

[OBenz94]

Hello
I’m currently working on a project where i would like to use your vivid software package to solve a QP for my MPC.
I would like to ask if there is an improvement in the sense of having a quadratic constraints as inequality.
Thank you in advance.

[apete]

You're asking about quadratically constrained quadratic programs (QCQP) right?

You can model it using ExpressionsBasedModel, but currently none of the built in solvers can handle that model. You need to either extend the functionality in the org.ojalgo.optimisation.convex package or use some 3:d party solver.

[OBenz94]

Yes QCQP, as shown in the attached picture.
i have seen in the org.ojalgo.optimisation.convex package, the ActiveSetSolver. I think that could solve the problem. I'm trying to understand the code so i can call and use ExpressionsBasedModel.

[apete]

No, the ActiveSetSolver can only handle linear constraints.

[OBenz94]

i'm soory, yes the constraint in my problem is a linear inequality as shown in the attached picture. but the cost function is quadratic.

[apete]

Then there's no problem. Just describe the problem using ExpressionsBasedModel and call minimise or maximise.

[OBenz94]

Thank you so much for the reply.
I have started writing the code using ExpressionBasedModel and come to the linear inequality constraint as shown in this line:
Expression constr = model.addExpression("Constraint");
// theta is vector and omegaMatrix2D is the matrix
constr.setLinearFactors(theta, omegaMatrix2D); // the left side of the inequality
constr.upper(omegaVector); // the right side of the inequality

However it seems that upper() method doesn't accept a vector and accept only a scalar variable.
There is any other way to use a vector?

[OBenz94]

Hello, I have write this example with arbitrary matrices but unfortunately i get 0 as optimum in both variables:

public static void main(String[] args) {
    
    // Problem data
    double[][] phiMatrix = {{4.0, 1.0}, {6.0, 2.0}};
    RawStore phiMatrixa = RawStore.wrap(phiMatrix);
    Access2D<Double> phiMatrix2D = phiMatrixa;

    double[] phiVector = {1.0, 6.0};
    RawStore phiVectora = RawStore.wrap(phiVector);
    Access1D<Double> phiVector1D = phiVectora;
    
    
    double[][] omegaMatrix = {{6.0, 1.0}, {1.0, 0.0}, {2.0, 1.0}};
    RawStore omegaMatrixa = RawStore.wrap(omegaMatrix);
    Access2D<Double> omegaMatrix2D = omegaMatrixa;
    
    double[] omegaVector = {2.0, 7.0, 4.0};
    RawStore omegaVectora = RawStore.wrap(omegaVector);
    Access1D<Double> omegaVector1D = omegaVectora;
    
    // Create model and variables
    ExpressionsBasedModel model = new ExpressionsBasedModel();
    List<Variable> theta = new ArrayList<>();
    theta.add(model.addVariable("theta_1"));
    theta.add(model.addVariable("theta_2"));
    
    // Set objective
    Expression expr = model.addExpression("Objective");
    expr.setQuadraticFactors(theta, phiMatrix2D);
    expr.setLinearFactors(theta, phiVector1D);
    
 // 3. Add constraints properly - one constraint per row
    for (int i = 0; i < omegaMatrix2D.countRows(); i++) {
        Expression constraint = model.addExpression("Constraint_" + i);
        Access1D<Double> coeffArray = omegaMatrix2D.rows(i);
        
        // Set all linear factors at once for this constraint
        constraint.setLinearFactors(theta, coeffArray);
        
        // Set individual upper bound for this constraint
        constraint.upper(omegaVector1D.doubleValue(i));
    }

    // Solve and print results
    Optimisation.Result resultt = model.minimise();
    
    
    // theta.forEach(v -> System.out.printf("%s = %.4f\n", v.getName(), v.getValue()));
    
    System.out.println(resultt.getState().isFeasible());
    
    System.out.println("theta_1: " + resultt.doubleValue(0));
    System.out.println("theta_2: " + resultt.doubleValue(1));
    
    System.out.println("Objective Function Value: " + resultt.getValue());

}

Do i miss something ?

[apete]

In that model there is no objective.

Have a look at this example: https://www.ojalgo.org/2019/05/the-diet-problem/

It's for an LP, but it shows how constraints and the objective are declared.

Also, you could read the javadoc for ExpressionsBasedModel.

[OBenz94]

I have try to read the example and take a look on other examples.
The sizes of my matrices are big (in my case the Theta vector is in the size of 80x1). i would like to know if there is a methods where it take the whole matrices and vectors instead of declaring entries one by one. Since I'm trying to optimize a cost function for a model predictive control.

[apete]

ExpressionsBasedModel is not designed to be used with matrices. The intention is more that you build an ExpressionsBasedModel instead of a set of matrices.

If you use ConvexSolver.Builder you miss important features like pre-solve and parameter scaling.