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Simulating human motion is a complex problem due to redundancy of the human musculoskeletal system. The concept of task-based motion prediction using single- or multi-objective optimization techniques provides a viable approach for predicting intermediate motions of digital humans. It is shown that task-based motion prediction is in fact a numerical optimal control problem. Alternative formulations for simulation of human motion are possible and can be solved by modern nonlinear optimization methods. Three techniques based on state variable elimination, direct collocation and differential inclusion are presented and compared. The basic idea of the formulations is to treat different combinations of the state variables, such as the joint profiles and torques or their parametric representations as independent variables in the optimization process.