In this note, we consider the problem of computing the parameters (or weights) of an optimal control objective function given optimal closed-loop state and control trajectories. We establish a method of inverse optimal control that exploits the discrete-time minimum principle. Under a testable matrix rank condition, our proposed method is guaranteed to recover the unknown objective-function parameters of finite-horizon discrete-time nonlinear optimal control problems. (C) 2017 Elsevier Ltd. All rights reserved.