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.