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From OpenOpt

Quadratically Constrained Quadratic Problems (QCQP)

subjected to

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• OpenOpt QCQP example
• (since v. 0.50) FuncDesigner QCQP example

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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).

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Attention:
Some optimization frameworks or standalone solvers (beyond OpenOpt) use other definition instead: .
Thus if you'll translate some code to or from OpenOpt, ensure you put correct sign before s_i.
You shouldn't care of it if you code FuncDesigner model.

See also: QP, MIQCQP, MIQP, SDP, SOCP, SparseMatrices