I try to find how cvx cast a qcqp into a SOCP using Ecos solver. I know how to cast second order constraint in G and h matrix. But I have also a quadratic objective which looks like : obj(x) = f^T x + x^T Q x. Now I just introduce t as a new variable such that my objective becomes linear obj(x,t) = f^T x +t. Then I have a new constraint which is x^T Q x<= t and I have an augmented optimization program. CVX dost not seem to do that and I do not understand what is doing. Someone has an idea?