This thesis presents a new approach for solving the non-convex optimization problem of locating a semi-obnoxious facility. By applying the duality theory by Toland and Singer for d.c. optimization problems the existence of optimal solutions is studied. Duality assertions, geometrical properties and discretization results are stated and proven. Moreover, this thesis considers the more general case of a constrained location problem. It is shown that most of the results obtained for the unconstrained location problem can be generalized to the constrained case. The obtained results are applied in order to formulate algorithms, which determine exact solutions by leading back the non-convex optimization problem to a finite number of convex problems. The developed algorithms are implemented as Matlab functions. Although, a scalar optimization problem is considered, this thesis shows interesting relations to the fields of linear vector optimization and geometric duality theory.