The discrete-time maximum principle : a survey and some new results |
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Authors: | ZBIGNIEW NAHORSKI HANS F RAVN RENÉ VICTOR VALQUI VIDAL |
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Affiliation: | 1. Polish Academy of Sciences , Systems Research Institute , Poland;2. The Institute of Mathematical Statistics and Operations Research , The Technical University of Denmark , Denmark. |
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Abstract: | In this paper we present 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 ore exposed. Following the review, we 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. |
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