Proof of the Maximum Principle

  • Leonard D. Berkovitz
Part of the Applied Mathematical Sciences book series (AMS, volume 12)


This chapter is devoted to the proof of the maximum principle, Theorem V.3.1. We shall actually prove a theorem that is more general than the maximum principle and shall obtain the maximum principle as a special case of this theorem. An essential property of an optimal trajectory is used to motivate the introduction of a concept called -N extremality. A necessary condition for -N extremality is then stated (Theorem 3.1 of this chapter), and it is shown how this implies Theorem V.3.1.


Maximum Principle Compact Interval Relative Interior Optimal Pair Fundamental Matrix Solution 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Leonard D. Berkovitz
    • 1
  1. 1.Division of Mathematical SciencesPurdue UniversityWest LafayetteUSA

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