Summary: A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in \(\mathbb{R}^{n}\) is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem.