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About: Quadratically constrained quadratic program     Goto   Sponge   NotDistinct   Permalink

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In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form where P0, …, Pm are n-by-n matrices and x ∈ Rn is the optimization variable. If P0, …, Pm are all positive semidefinite, then the problem is convex. If these matrices are neither positive nor negative semidefinite, the problem is non-convex. If P1, … ,Pm are all zero, then the constraints are in fact linear and the problem is a quadratic program.