  In this paper we analyze theoretical properties of bi-objective
convex-quadratic problems. We give a complete description of their Pareto set
and prove the convexity of their Pareto front. We show that the Pareto set is a
line segment when both Hessian matrices are proportional. We then propose a
novel set of convex-quadratic test problems, describe their theoretical
properties and the algorithm abilities required by those test problems. This
includes in particular testing the sensitivity with respect to separability,
ill-conditioned problems, rotational invariance, and whether the Pareto set is
aligned with the coordinate axis.
