We consider mixed-integer programs with non-convex objectives that are modelled with indicator variables. Because this modelling typically requires the use of big-M values, such programs often have weak linear programming relaxations. The dual bound in a branch-and-bound tree therefore improves only slowly, which results in very long solution times. To strengthen the dual bound we partition the problem and then apply Lagrangean decomposition in order to obtain independent subproblems. We show for an application to support vector machines with ramp loss, that the dual bound can be improved compared to the bound obtained from a full mixed-integer programming formulation. Moreover, the subproblems can be efficiently solved in parallel.