A smart choice of contact forces between robotic grasping devices and objects is important for achieving a balanced grasp. Too little applied force may cause an object to slip or be dropped, and too much applied force may cause damage to delicate objects. Prior methods of grasping force optimization in literature have mostly assumed grasp only at the fingertips but have rarely considered how the whole hand grasps more common to anthropomorphic hands affect the optimization of grasping forces. Further, although numerical examples of grasping force optimization methods are routinely provided, it is often difficult to compare the performance of separate methods when they are evaluated using different parameters, such as the type of grasping device, the object grasped, and the contact model, among other factors. This paper presents three optimization approaches (linear, nonlinear, and nonlinear with linear matrix inequality (LMI) friction constraints) which are compared for an anthropomorphic hand. Numerical examples are provided for three types of grasp commonly performed by the human hand (cylindrical grasp, tip grasp, and tripod grasp) using both soft finger contact and point contact with friction models. Contact points between the hand and the object are predetermined. Results are compared based on their accuracy, computational efficiency, and other various benefits and drawbacks unique to each method. Future work will extend the problem of grasping force optimization to include consideration for variable forces and object manipulation.