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.