Abstract. Home-Away Assignment problems are naturally cast as quadratic programming models in binary variables. In this work we compare alternative formulations. First, we propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. By linearizing the quadratic objective function, we get two more alternative models to be compared with the quadratic ones. Numerical experiments exhibit the characteristics of each model. Palavras-chave.Sport scheduling, HA-assignment, Integer linear programming, Integer quadratic programming.

We present a Riemannian Conjugate Gradient (RCG) algorithm to solve the Joint Diagonalization Problem in Stiefel manifolds. We use the special structure of this manifold to build a procedure which avoids extra-calculations associated to vector transportation. Numerical experiments which compare our algorithm with other known procedures are also provided.