On the maximum priciple for nonlinear discrete-time systems

It was shown in a previous paper that Halkin's maximum principle for difference equations linear in the state could be generalized by relaxing a convexity requirement to directional convexity. We show here that Halkin's results for difference equations not necessarily linear in the state may also be generalized. The new proof uses some rather simple arguments. The proof is based on a condition characterizing the optimal solution. This condition may be used to strengthen the maximum principle in the abnormal case.