I don't know if someone can help here as the target community may not be so wide, but I will give it a try.
I'm practicing with the open-source C++ CasADi library for optimization and I'm struggling with the implementation of a quadratic programming (QP) problem with a linear constraint. Unfortunately, the official documentation regarding the proper syntax for C++ is only partial and deducing it from the other languages (Python, MATLAB) is not always that easy.
To make it short, inspired also by the example programs of the library, I wrote a minimal replicable code for a trivial QP problem such as:
casadi::SX xs = casadi::SX::sym("xs");
casadi::SX ys = casadi::SX::sym("ys");
casadi::SX fs = (xs) * (xs) + (ys) * (ys);
casadi::SX gs = xs - 3.0;
casadi::SXDict qp_problem = { {"x",casadi::SX::vertcat({xs,ys})}, {"f", fs}, {"g",gs}};
casadi::Function qp_solution = casadi::qpsol("QPproblem", "qrqp", qp_problem);
std::vector<double> x0 = { 10,10 };
casadi::DMDict arg = { {"x0",x0} };
std::cout << "Extracting the solution ... " << std::endl;
casadi::DMDict res = qp_solution(arg);
std::cout << "res[x] = " << res["x"] << std::endl;
According to the official documentation, the variable gs specifies a linear inequality constraint as xs - 3.0 >= 0, while fs is the cost function to minimize.
As such, I would expect that the resulting minimum value for the x (i.e., res[x]) was (3,0) in virtue of the constraint. Instead, the output of the above-reported code returns the pair (0,0), i.e., as if the constraint function gs was not taken into account. I've also tried in changing the vertex of the paraboloid in fs (i.e., by testing fs = (xs-x0) * (xs-x0) + (ys-y0) * (ys-y0)), obtaining always the pair (x0,y0) as minimum, independently on the expression of the constraint gs.
Is there anything in the syntax that I'm possibly writing wrongly, or something in the discussion that I'm uncorrectly considering?
Thanks in advance for any help