| # SOCPs include QCQps as a Special Case Theorem: QCQPs as SOCPs The quadratically constrained quadratic programming problem where , , , can be expressed as an SOCP with rotated second-order cone constraints: Proof: We first represent the problem in epigraph form: Now, a constraint of the form is equivalent to the existence of such that where is the square-root of the PSD matrix . Applyng this to the constraints of the above formulation, we obtain an equivalent representation of the original QCQP: The above can be written as given in the theorem, as claimed.