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A quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions.
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Complexity of convex quadratically constrained quadratic programming (QCQP)
According to the Wikipedia article at http://en.wikipedia.org/wiki/NP-hard it is NP-hard. The Wikipedia article gives as a reference a book which is available at http://www.stanford.edu/~boyd/cvxbook/ …