The Discrete-Time Maximum Principle - a survey and some new results

Presents a review of the development of the discrete maximum principle. In the presentation, the emphasis is on a geometrical interpretation. The crucial assumptions in the theory developed are pointed out, and the attempts to overcome the limitation in the resulting theorems are exposed. Following the review, the authors present a new approach to optimization of the multi-stage optimization problems called the `upper boundary approach'. The classical methods of solving this problem are shown to fit smoothly into the new approach. Moreover, using this approach a number of new results have been developed, among these a new generalized version of the discrete maximum principle. The new version does not require the assumption of directional convexity