A numerical technique is presented to evaluate the maximum power that can be absorbed from a linear three-dimensional multi-degree-of-freedom system. A weighted global constraint is imposed on the system's excursions to ensure that the assumptions of linear theory remain valid. The numerical solution gives good agreement with known semi-analytical results for the case of a heaving hemisphere. A surging hemisphere is also studied, from which the relative merits of heave and surge become apparent. In the two-degree-of-freedom case, the numerical procedure selects the optimal combination of heave and surge. The technique is then applied to a solo-duck in up to six degrees of freedom in oblique waves. The possibility of utilising the point absorber effect in realistic seas is assessed. The significance of singularities in the damping matrix is discussed.