QCQP

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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: currently only cplex (license: commercial / full version free for educational / free 90-days trial with limitations nVars/nConstraints up to 500).
  • 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).
AttentionAttention:
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, but currently FuncDesigner can't handle QCQPs.
See also: QP, MIQCQP, MIQP, SDP, SOCP
Retrieved from "http://openopt.org/QCQP"
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