the aim of this talk to show that several quantities: as the spectral radius of weakly irreducible tensors, maximum of d-homogeneous polynomial with nonnegative coefficients in the unit ball of the d-h¨older norm, are polynomially computable. this computability result is proven for a larger class of minimum of certain convex functions in r n, which was considered by several authors. this is a joint work with stephane gaubert, inria and centre de math´ematiques appliqu´ees (cmap), ecole polytechnique, ip paris, france.