This talk will focus on the inverse problem in optimal control theory: Given the constraints that a control system must satisfy and examples of optimal solutions, determine the cost function that is being minimized. In this problem, the cost function is assumed to be a linear combination of known basis functions multiplied by an unknown weight vector, which must be inferred. Previous solution methods have two main drawbacks: (1) they require the optimal control problem to be solved for many candidate weight vectors, and (2) these methods only produce one of the possibly many weight vectors that are consistent with the example solutions. In this talk, we will formulate the inverse optimal control problem in a way such that all possible weight vectors can be found by solving a single linear-quadratic optimal control problem (even if the original problem is nonlinear).