One of the basic requirements in grasping and manipulation of objects is the determination of a suitable set of grasping forces such that the external forces and torques applied on the object are balanced and the object remains in equilibrium. This report presents a new mathematical approach to efficiently obtain the optimal solution of this problem using the dual theorem of non-linear programming. The problem is modeled such that the basic convexity property necessary to apply the dual theorem is satisfied and, then, it is transformed into another one much easier to be solved. Three examples showing the efficiency and accuracy of the proposed methodology are included in the report.