Extremal Problems in Banach Spaces

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


This chapter deals with the extension of the Tent Method to Banach spaces. The Abstract Extremal Problem is formulated as an intersection problem. The subspaces in the general positions are introduced. The necessary condition of the separability of a system of convex cones is derived. The criterion of separability in Hilbert spaces is presented. Then the analog of the Kuhn–Tucker Theorem for Banach spaces is discussed in detail.


Hilbert Space Banach Space Convex Body General Position Convex Cone 
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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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