QCQP

$\mathbf{\frac{1}{2} x^T Hx + f^T x \rightarrow min}$
subjected to
$\mathbf{lb \le x \le ub}$
$\mathbf{A x \le b}$
$\mathbf{A_{eq} x = b_{eq}}$
$\mathbf{\forall i = 0...I: \frac{1}{2}x^T Q_i x + p_i ^T x + s_i \le 0 }$

Available QCQP solvers:

• cplex (license: commercial / full version free for educational / free 90-days trial with limitations nVars/nConstraints up to 500), convex problems only
• interalg (preferably for non-convex QCQP)

If someone is ready to pay for it, free and rather good QCQP solvers can be build around Algencan and ralg/gsubg. Also, in more long-term future IPOPT could be involved, but current IPOPT-Python connection can't handle 2nd derivatives (that is very important for handling QCQPs).

Attention:
Some optimization frameworks or standalone solvers (beyond OpenOpt) use other definition instead: $\mathbf{\frac{1}{2}x^T Q_i x + p_i ^T x \le s_i }$.
Thus if you'll translate some code to or from OpenOpt, ensure you put correct sign before si.
You shouldn't care of it if you code FuncDesigner model.