T HE purpose of this Note is to concisely discuss the analytical aspects of a number of methods for obtaining initial Lagrange multipliers for the shooting method. Because the ultimate goal is to use the shooting method, the partial derivatives of the state equation with respect to the time, the state, and the control are available and can be used to enhance the performance of these methods. The methods considered are parameterizing the control within the shooting method, direct shooting, collocation (direct transcription), pseudospectral method, dynamic programming, and adjoint-control transformation. The intent is to discuss each of these methods briefly to present their important features. A standard optimal control problem without path constraints is stated, as are the corresponding optimality conditions. Next, a brief derivation of the shooting method is presented to show what informationwould be available for initial multiplier prediction and to show how to parameterize the control within the shooting method. Then the other methods are discussed briefly.