New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with d ≥ 3) will be presented in this work. Each model features a non smooth objective function but a convex set of feasible solutions. All these models are theoretically equivalent. From these models, six mixed integer linear and nonlinear relaxations will be considered. Each relaxation has the same set of feasible solutions as the model from which it is derived. Finally, preliminary computational results highlighting the main features of the presented relaxations will be discussed.