Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in $$\mathbb {R}^d$$

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