| # SOCPs include QPs as Special Case The quadratic program (QP) where , can be cast as an SOCP, as follows. First we introduce a new variable and a new linear equality. With , we express the QP as Then, we add two new scalar variables, and a rotated cone constraint, to handle the second term in the objective. The QP bears the form The above is indeed an SOCP: The first constraint is a rotated cone constraint; The second and the third a affine equalities; The last constraints are ordinary affine inequalities.