Nonconvex optimization

[Vinícius Motta]

I am trying to model an ACOPF model with the rectangular form with YALMIP(meaning complex number variables and complex number constraints).

However, when I try to solve my model using FMINCON, I always have the following error:

Model creation failed (Only 1- and inf-norms can be used in a nonconvex fashion)

Upon further inspection, it is clear that the problem is when I try to add any constraints with norm(Variable,1) <= Bound or A + B + norm(Variable,1) == Value. On the Yalmip documentation/tutorials, I do find documentation about using norm and it seems that I'm using as it should be used. So, I decided to post here to see if anyone could help me in figuring out why does this problem happen.

[Vinícius Motta]

Sorry, when I mean the norm, I meant abs, not norm 1, since I'm using the abs function on complex numbers.

[Johan Löfberg]

the 1-norm of a complex matrix involves 2-norms

[Vinícius Motta]

That is what I thought. In other words, I can't solve a nonconvex optimization problem that involves constraints with norm of complex variables, can I?

[Johan Löfberg]

You would have to formulate it as a nonconvex quadratic problem instead, i.e. instead of using norm(x,1) == r, you would have to use like s.^2 == real(x).^2 + imag(x).^2, sum(s)==r, or something like that