Mathematical Background

  • Konstantin Kogan
  • Eugene Khmelnitsky
Part of the Applied Optimization book series (APOP, volume 43)


The methodology suggested in this book is based on three mathematical tools — optimal control, combinatorics and mathematical programming — which are traditionally related to separate areas of research and application. The methodology involves, first, investigating a continuous-time problem with the aid of the maximum principle and then reducing it to a discrete combinatorial or mathematical programming problem solvable in polynomial time. The following sections present selected combinatorics, the maximum principle and a constructive approach for integrating both mathematical tools.


Maximum Principle Optimal Control Problem Source Node Planning Horizon Linear Differential Equation 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Konstantin Kogan
    • 1
  • Eugene Khmelnitsky
    • 2
  1. 1.Department of Computer ScienceCenter for Technological EducationHolonIsrael
  2. 2.Department of Industrial EngineeringTel-Aviv UniversityTel-AvivIsrael

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