The Tent Method in Finite-Dimensional Spaces

  • Vladimir G. Boltyanski
  • Alexander S. Poznyak
Part of the Systems & Control: Foundations & Applications book series (SCFA)


The Tent Method is shown to be a general tool for solving a wide spectrum of extremal problems. First, we show its workability in finite-dimensional spaces. Then topology is applied for the justification of some results in variational calculus. A short historical remark on the Tent Method is made and the idea of the proof of the Maximum Principle is explained in detail, paying special attention to the necessary topological tools. The finite-dimensional version of the Tent Method allows one to establish the Maximum Principle and to obtain a generalization of the Kuhn–Tucker Theorem in Euclidean spaces.


Maximum Principle Extremal Problem Variational Calculus Conditional Extremum Tucker Theorem 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir G. Boltyanski
    • 1
  • Alexander S. Poznyak
    • 2
  1. 1.CIMATGuanajuatoMexico
  2. 2.Automatic Control DepartmentCINVESTAV-IPNMéxicoMexico

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