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Quadratically Constrained Quadratic Problems (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).

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.
See also: QP, MIQCQP, MIQP, SDP, SOCP, SparseMatrices
Retrieved from "http://openopt.org/QCQP"
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