How to solve this problem? Error using == Quadratic constraints not supported

Hi everyone

I have a optimazation problem using "optimproblem". The problem is constraint. The constraint I need is x*x + y*y ==1.

        x = optimvar('x');
        y = optimvar('y');
        prob = optimproblem;
        prob.Objective = (((x*((K*x)+(K*y)))+(y*((K*x)+(K*y)))) - ((2*F*x))+((2*F*y)));
        prob.Constraints.cons1 = x*x + y*y == 1;
        sol = solve(prob);

The error messages as follows

Error using ==

Quadratic constraints not supported.

error in ..... (Line 237)

prob.Constraints.cons1=x*x + y*y ==1;

could you help me to fix this problem?

Thanks! Intho

Answer 1

[Abdolkarim Mohammadi]

QP = Quadradic Programming = Quadradic objective function and linear constraints.

QCQP = Quadratically Constrained Quadratic Programming = Quadradic objective function and quadradic constraints.

quadprog() solves QP problems, but you are defining a QCQP problem. QCQP can be solved using the combination of quadprog() and fmincon() as described in the following:

https://www.mathworks.com/help/optim/ug/linear-or-quadratic-problem-with-quadratic-constraints.html

Answer 2

[Walter Roberson]

x*x + y*y == 1

Reduce the number of variables by replacing y with +/- sqrt(1-x^2) . Run twice, once with y being the positive root, and once with y being the negative root, and choose the best of the two.

If K and F are independent of x and y, then you can use calculus: differentiate with respect to x and solve for the zeros.

The roots for the + and - branch come out nearly exactly the same. Both of the branches have roots

(-F +/- sqrt(-F^2 + 2*K^2))/(2*K)

The + branch has root -1/sqrt(2) and the - branch has root +1/sqrt(2)

You would want to verify that these roots are indeed minima and not maxima.