An essential ingredient of our algorithms for solving QP and QCQP problems is the Euclidean projection on the convex set defined by separable convex constraints. Bound, spheric, and elliptic constraints are considered. Here, we provide nontrivial bounds on the decrease of f along the projected-gradient path in terms of bounds on the spectrum of its Hessian matrix \({\mathsf {A}}\) . These results allow for the effective combination of gradient projection with the conjugate gradient method.